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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+67x^76+40x^77+128x^78+134x^79+241x^80+352x^81+383x^82+560x^83+606x^84+656x^85+875x^86+1062x^87+1224x^88+1308x^89+1287x^90+1300x^91+1174x^92+1056x^93+886x^94+730x^95+541x^96+496x^97+336x^98+240x^99+150x^100+168x^101+132x^102+58x^103+68x^104+20x^105+32x^106+12x^107+19x^108+26x^110+5x^112+9x^114+1x^118+1x^122

The gray image is a linear code over GF(2) with n=360, k=14 and d=152.
This code was found by Heurico 1.16 in 33.9 seconds.