The generator matrix

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

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+48x^44+156x^45+159x^46+372x^47+281x^48+518x^49+304x^50+518x^51+332x^52+516x^53+224x^54+302x^55+81x^56+136x^57+61x^58+18x^59+23x^60+16x^61+12x^62+6x^63+1x^64+2x^65+7x^66+1x^68+1x^70

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 0.683 seconds.