The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+42x^73+131x^74+230x^75+387x^76+522x^77+664x^78+812x^79+899x^80+1048x^81+1244x^82+1300x^83+1385x^84+1540x^85+1635x^86+1724x^87+1784x^88+1850x^89+1800x^90+1808x^91+1784x^92+1644x^93+1518x^94+1374x^95+1203x^96+1004x^97+870x^98+694x^99+558x^100+434x^101+262x^102+210x^103+156x^104+94x^105+57x^106+40x^107+29x^108+12x^109+8x^110+5x^112+2x^113+2x^114+1x^116+1x^134

The gray image is a linear code over GF(2) with n=178, k=15 and d=73.
This code was found by Heurico 1.11 in 80.9 seconds.