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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+26x^86+117x^88+16x^89+200x^90+32x^91+207x^92+216x^93+199x^94+320x^95+217x^96+368x^97+215x^98+544x^99+193x^100+352x^101+197x^102+128x^103+153x^104+64x^105+120x^106+97x^108+8x^109+46x^110+24x^112+12x^114+7x^116+3x^118+7x^120+4x^122+1x^126+1x^130+1x^152

The gray image is a linear code over GF(2) with n=392, k=12 and d=172.
This code was found by Heurico 1.16 in 3.08 seconds.