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

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+30x^76+118x^77+194x^78+254x^79+341x^80+422x^81+527x^82+656x^83+771x^84+836x^85+1057x^86+1240x^87+1157x^88+1248x^89+1286x^90+1234x^91+1115x^92+858x^93+685x^94+544x^95+447x^96+356x^97+258x^98+214x^99+188x^100+94x^101+68x^102+66x^103+40x^104+30x^105+20x^106+16x^107+4x^108+6x^109+2x^112+1x^122

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 31.5 seconds.