The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 0 1 1 1 1 0 X 0 X 0 1 X X 1 1 1 X X X 1 1 0 1 1 0 1 1 0 X X X X X X 1 1 1 0 0 X 1 X X 1 1 0 1 0 1 0 1 1 1 1 X 1 1 0 1 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X X+1 X 1 1 1 0 1 X+1 X+1 0 X+1 X+1 1 1 X X X+1 1 1 1 1 1 X 1 X 1 X 1 1 X X X 1 1 0 X 0 0 1 X X 0 1 X X 1 X 0 1 X 0 0 X X 1 X+1 0 0 0 1 1 0 X+1 X+1 X X 0 X X 1 1 1
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 0 X X 1 0 1 1 0 X+1 1 X+1 0 X+1 X 0 X 0 1 1 X+1 X+1 X+1 X+1 0 X X+1 0 1 X+1 1 1 X 0 1 0 1 X 1 X X+1 1 X X 1 1 X X+1 0 0 1 X 1 1 X 1 0 X 0 X 1 1 1 X 1 0 1
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X X+1 0 1 X 0 X 1 X 1 X+1 X 0 X+1 X+1 X+1 X X X+1 0 0 1 X 0 0 0 X 0 X+1 X+1 1 X 1 1 0 1 1 X+1 X 1 X+1 X 1 X+1 X+1 X 0 0 X X+1 0 0 0 X 0 1 X+1 1 X+1 X+1 1 0 0 X 0 0 X 1 X+1 1 X+1 1 0 X
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 X 1 X X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 X 1 0 1 X+1 0 X X X+1 X+1 X+1 X 0 X 0 X 1 1 X+1 X X X X+1 X+1 0 X X+1 X+1 X X X 0 X X+1 X X X+1 X X+1 1 0 0 X X+1 0 X 1 X X+1 1 X+1 X+1 1 X+1 X+1 1 1 X X+1 X
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X 0 X+1 X+1 0 X+1 0 1 X 0 1 X+1 X+1 X+1 X X+1 X+1 X 0 0 X+1 1 1 0 0 X 1 1 1 0 X 1 0 X+1 X 0 0 X X+1 X+1 0 X 1 X+1 0 0 1 X 1 0 0 X+1 1 X X X+1 1 1 X 1 1 X+1 0 0 X+1 1 1 X+1 X+1 0 X 0 0 1
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 X 0 X 0 X 0 0 X X X X 0 0 X 0 0 0 0 0 0 X X 0 X 0 X X 0 X X X X 0 X 0 X 0 X X 0 0 X 0 0 0 X 0 X 0 X 0 0 0 X X 0 0 0 0 0 0 X

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+203x^76+462x^78+672x^80+816x^82+793x^84+854x^86+845x^88+792x^90+741x^92+682x^94+566x^96+348x^98+211x^100+126x^102+59x^104+12x^106+4x^108+4x^110+1x^112

The gray image is a linear code over GF(2) with n=176, k=13 and d=76.
This code was found by Heurico 1.10 in 4.47 seconds.