The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+61x^80+116x^81+285x^82+230x^83+386x^84+240x^85+350x^86+216x^87+430x^88+246x^89+394x^90+182x^91+335x^92+172x^93+216x^94+78x^95+49x^96+14x^97+20x^98+14x^99+11x^100+8x^101+10x^102+14x^103+6x^104+4x^105+1x^106+2x^107+3x^110+1x^118+1x^120

The gray image is a linear code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 1.67 seconds.