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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+100x^78+266x^80+8x^81+466x^82+44x^83+748x^84+140x^85+898x^86+340x^87+1159x^88+644x^89+1617x^90+888x^91+1781x^92+856x^93+1663x^94+616x^95+1284x^96+368x^97+879x^98+156x^99+626x^100+28x^101+362x^102+4x^103+208x^104+4x^105+119x^106+54x^108+28x^110+8x^112+7x^114+6x^116+4x^118+1x^120+1x^124+1x^126+1x^128

The gray image is a linear code over GF(2) with n=368, k=14 and d=156.
This code was found by Heurico 1.16 in 34.2 seconds.