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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+70x^76+104x^77+167x^78+290x^79+315x^80+430x^81+498x^82+634x^83+821x^84+926x^85+1096x^86+1190x^87+1194x^88+1234x^89+1210x^90+1020x^91+1040x^92+894x^93+745x^94+678x^95+456x^96+380x^97+248x^98+224x^99+147x^100+100x^101+109x^102+56x^103+42x^104+28x^105+20x^106+2x^107+10x^108+2x^110+2x^111+1x^118

The gray image is a linear code over GF(2) with n=356, k=14 and d=152.
This code was found by Heurico 1.16 in 31 seconds.