The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+72x^80+216x^81+279x^82+450x^83+371x^84+456x^85+304x^86+368x^87+206x^88+290x^89+196x^90+184x^91+160x^92+162x^93+91x^94+80x^95+73x^96+54x^97+17x^98+38x^99+13x^100+6x^101+4x^102+4x^106+1x^110

The gray image is a linear code over GF(2) with n=348, k=12 and d=160.
This code was found by Heurico 1.16 in 1.31 seconds.