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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+54x^74+98x^75+179x^76+234x^77+305x^78+338x^79+366x^80+362x^81+346x^82+426x^83+434x^84+420x^85+438x^86+402x^87+420x^88+436x^89+349x^90+410x^91+356x^92+342x^93+278x^94+254x^95+259x^96+202x^97+148x^98+102x^99+84x^100+40x^101+50x^102+14x^103+10x^104+8x^105+15x^106+4x^107+3x^108+4x^109+1x^110

The gray image is a linear code over GF(2) with n=174, k=13 and d=74.
This code was found by Heurico 1.10 in 4.36 seconds.