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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+181x^74+500x^76+640x^78+757x^80+876x^82+839x^84+814x^86+815x^88+770x^90+695x^92+568x^94+371x^96+187x^98+98x^100+53x^102+20x^104+6x^106+1x^110

The gray image is a linear code over GF(2) with n=172, k=13 and d=74.
This code was found by Heurico 1.10 in 4.33 seconds.