The generator matrix

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

generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+116x^44+72x^45+260x^46+176x^47+408x^48+312x^49+500x^50+416x^51+549x^52+312x^53+332x^54+176x^55+301x^56+72x^57+60x^58+18x^60+5x^64+5x^68+5x^72

The gray image is a linear code over GF(2) with n=204, k=12 and d=88.
This code was found by Heurico 1.16 in 0.761 seconds.