The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+288x^81+194x^82+630x^83+241x^84+650x^85+138x^86+408x^87+145x^88+364x^89+104x^90+262x^91+88x^92+202x^93+42x^94+136x^95+33x^96+80x^97+34x^98+32x^99+3x^100+16x^101+4x^103+1x^104

The gray image is a linear code over GF(2) with n=348, k=12 and d=162.
This code was found by Heurico 1.11 in 55.4 seconds.