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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+56x^77+115x^78+192x^79+236x^80+324x^81+398x^82+462x^83+531x^84+714x^85+901x^86+1030x^87+1279x^88+1328x^89+1348x^90+1356x^91+1285x^92+1038x^93+885x^94+728x^95+526x^96+440x^97+307x^98+226x^99+173x^100+154x^101+107x^102+82x^103+52x^104+36x^105+26x^106+20x^107+11x^108+6x^109+5x^110+1x^112+1x^114+2x^118+1x^126+1x^136

The gray image is a linear code over GF(2) with n=360, k=14 and d=154.
This code was found by Heurico 1.16 in 31.9 seconds.