The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 X X X 1
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 0 0 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 0 2X 2X 0 0 0 2X 2X 2X 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 2X 0 0 2X
0 0 0 2X 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 0 2X 0 2X 0 2X 2X 0 0 0 0 2X 0 0 2X 2X
0 0 0 0 2X 0 0 0 0 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 2X 0 0 2X 0 0 2X
0 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 0 2X 0 0 2X 0 0 0 0 0 2X 2X 0 2X 0 0 0 2X 2X 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0 2X 0 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 0 2X 2X 0 0
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 0 2X 0 2X 0 2X 0 2X 0 0 2X 2X 2X 2X 0 0 2X 0 0 2X 2X 0 2X 0 2X 2X 2X 0 0 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 2X
0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 0 0 0 2X 0 2X 0 2X 2X 0 2X 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 0 0 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 0 0 2X
generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+65x^76+8x^78+102x^80+80x^82+1536x^83+127x^84+40x^86+48x^88+30x^92+9x^96+1x^100+1x^156
The gray image is a code over GF(2) with n=664, k=11 and d=304.
This code was found by Heurico 1.16 in 0.594 seconds.