The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+68x^78+106x^79+165x^80+204x^81+223x^82+226x^83+208x^84+242x^85+219x^86+232x^87+220x^88+208x^89+190x^90+186x^91+162x^92+164x^93+150x^94+132x^95+154x^96+134x^97+107x^98+94x^99+82x^100+56x^101+51x^102+42x^103+28x^104+14x^105+16x^106+4x^107+4x^108+2x^109+2x^115

The gray image is a linear code over GF(2) with n=178, k=12 and d=78.
This code was found by Heurico 1.10 in 1.19 seconds.