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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+56x^75+105x^76+160x^77+219x^78+310x^79+381x^80+416x^81+454x^82+546x^83+642x^84+586x^85+663x^86+646x^87+566x^88+480x^89+445x^90+440x^91+259x^92+182x^93+140x^94+142x^95+102x^96+66x^97+48x^98+30x^99+50x^100+24x^101+9x^102+6x^103+6x^104+6x^105+4x^106+1x^110+1x^122

The gray image is a linear code over GF(2) with n=344, k=13 and d=150.
This code was found by Heurico 1.16 in 8.37 seconds.