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 X X X X X X X X X X X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 1 1 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0
generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 87.
Homogenous weight enumerator: w(x)=1x^0+60x^87+175x^88+15x^92+4x^103+1x^116
The gray image is a code over GF(2) with n=704, k=8 and d=348.
This code was found by Heurico 1.16 in 0.484 seconds.