The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+60x^73+180x^74+266x^75+345x^76+440x^77+511x^78+574x^79+621x^80+706x^81+737x^82+760x^83+838x^84+836x^85+888x^86+914x^87+926x^88+898x^89+776x^90+800x^91+737x^92+672x^93+612x^94+506x^95+464x^96+374x^97+325x^98+216x^99+144x^100+100x^101+60x^102+54x^103+20x^104+10x^105+6x^106+6x^107+1x^142

The gray image is a linear code over GF(2) with n=174, k=14 and d=73.
This code was found by Heurico 1.10 in 16.6 seconds.