The generator matrix

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

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+36x^44+106x^45+254x^46+290x^47+346x^48+426x^49+416x^50+472x^51+412x^52+406x^53+302x^54+222x^55+205x^56+72x^57+38x^58+28x^59+17x^60+12x^61+12x^62+12x^63+4x^64+2x^65+2x^66+3x^68

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 0.65 seconds.