The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2  X  X  X  1  X X^2  0  1  X  1  1  1  1  1  1  1  1  1  1 X^2 X^2  1  0  0  X X^2 X^2  1  1  0 X^2  X X^2 X^2 X^2  X  1  0  X  1  1  1  1  0  1  1  X  1
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2  X X^2+X  X X^2 X^2 X^2+X X^2  0 X^2+X  X X^2+X X^2 X^2+X X^2+X  0 X^2+X X^2+X X^2 X^2+X  X  X  X X^2  X X^2  0 X^2+X  X  0  0 X^2+X  X X^2  X  X X^2+X X^2+X X^2 X^2  0 X^2+X  X  X  0 X^2 X^2 X^2+X  X  X X^2  X  X  X X^2+X  X  0  X X^2  X  0 X^2+X X^2+X X^2+X  0  X  X X^2  X  X  0
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X X^2  0 X^2+X  X  0 X^2+X  X X^2  X X^2+X  0  0 X^2  0 X^2+X X^2+X  X X^2+X X^2 X^2+X X^2 X^2  0 X^2+X  X  X  X  X X^2  0 X^2+X  X X^2+X X^2 X^2 X^2 X^2+X  X  0 X^2+X X^2 X^2  X X^2  X  X X^2  X  X X^2 X^2+X  X X^2+X X^2+X  0  0  X X^2  X  0  X  0  X X^2+X X^2+X  X  0  0 X^2+X  X  X  X  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+46x^74+62x^75+137x^76+142x^77+267x^78+300x^79+379x^80+498x^81+609x^82+722x^83+933x^84+1050x^85+1142x^86+1280x^87+1261x^88+1334x^89+1188x^90+1114x^91+881x^92+762x^93+531x^94+468x^95+336x^96+246x^97+219x^98+118x^99+121x^100+62x^101+66x^102+32x^103+36x^104+2x^105+16x^106+7x^108+8x^110+2x^112+2x^114+2x^118+1x^120+1x^124

The gray image is a linear code over GF(2) with n=352, k=14 and d=148.
This code was found by Heurico 1.16 in 32.5 seconds.