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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+73x^78+106x^79+188x^80+280x^81+314x^82+466x^83+548x^84+694x^85+767x^86+890x^87+1144x^88+1094x^89+1110x^90+1230x^91+1179x^92+1082x^93+1027x^94+938x^95+737x^96+608x^97+487x^98+332x^99+306x^100+268x^101+138x^102+100x^103+96x^104+56x^105+40x^106+28x^107+23x^108+12x^109+10x^110+6x^111+2x^112+2x^113+1x^114+1x^118

The gray image is a linear code over GF(2) with n=364, k=14 and d=156.
This code was found by Heurico 1.16 in 32.6 seconds.