The generator matrix

 1  0  1  1  1 X^2+X  1  0  1  1  1 X^2  1  1  X  1 X^2+X  1  1  1 X^2  1  1  1 X^2+X X^2  1  1  X  1 X^2  1 X^2+X  X  1  0  X  1  0  1 X^2+X  1  1 X^2  1  1  X  1  1  0  X
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1  X  1  1  X X+1  1 X^2  1 X+1  1  0  1 X^2+X X^2+1  0  1  1 X^2+X  1  1 X^2  1  1  1  1 X^2+X+1  1  1  X  1  0  1  1  X  0  X X+1 X^2+X X^2+X+1 X^2+X+1  X  0
 0  0  X  0 X^2+X  0  0  X X^2  X X^2 X^2+X X^2+X  0  0 X^2+X X^2+X  X  X X^2+X X^2 X^2 X^2  0 X^2+X  X X^2 X^2+X  0  X  0 X^2 X^2+X  0 X^2 X^2  0 X^2+X X^2+X  0 X^2  X  X X^2  0 X^2+X  X X^2+X X^2+X X^2  0
 0  0  0  X  0  0 X^2+X  X X^2+X  0 X^2+X X^2  X  0 X^2+X X^2 X^2+X X^2+X X^2+X X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2 X^2  X  0  X  X X^2+X X^2+X  X  X X^2  0 X^2 X^2  X  X X^2+X  X X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  0
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 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+90x^44+72x^45+288x^46+188x^47+479x^48+344x^49+505x^50+356x^51+472x^52+296x^53+339x^54+212x^55+218x^56+56x^57+83x^58+12x^59+40x^60+29x^62+10x^64+4x^66+2x^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 0.67 seconds.