The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1  0  X  X  1  X  1  1  0 X^2  0  1  X  1  X X^2 X^2+X  1  1  1  1  1 X^2+X X^2  1  1  1  X  0 X^2 X^2+X  X  X  0  1 X^2  X X^2+X  1  1
 0  1  0  0  X X^2 X^2+X  1 X+1 X^2+1  1 X^2+1  1  1 X^2  X  1  0 X^2+X  X X^2+X  1 X^2+X+1  1 X+1  1  X  1 X^2+1  0 X^2+X+1 X^2+X+1 X^2+X  1  1 X^2+1 X^2 X^2+X  1  1  1  1 X^2 X^2+X  0  X X^2+X X^2+X  1 X+1  0
 0  0  1  0  X X^2+1  1 X^2+1  0 X^2+1 X^2 X^2+X+1 X^2+X X+1  1 X+1  0  X  0  1  1 X^2+X+1  1 X^2 X^2+X X^2+1  X X^2+1 X^2+X+1  X X^2+X+1  0  1 X^2+X  X X^2+1  X X+1 X^2+X  1 X^2+1  1  X X^2  1 X^2+X+1 X^2  1 X^2 X^2+1  0
 0  0  0  1 X+1  1  X X^2+1 X^2+X X^2+X+1 X^2+X+1 X^2 X+1  X X^2+X+1  1 X^2+1 X^2+X X^2+1 X^2 X+1 X^2+1  1  0  0  X  1  0 X^2 X^2+X+1 X+1 X^2 X^2+X+1  1 X+1 X^2+X  0  X X^2+X+1 X^2+1 X^2+X X^2+X+1  1  1  0 X^2+1  1 X^2 X^2  1 X^2
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 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+70x^44+310x^45+327x^46+890x^47+563x^48+968x^49+614x^50+970x^51+626x^52+872x^53+443x^54+684x^55+296x^56+300x^57+85x^58+106x^59+40x^60+12x^61+2x^62+6x^63+4x^64+1x^66+2x^69

The gray image is a linear code over GF(2) with n=204, k=13 and d=88.
This code was found by Heurico 1.16 in 2 seconds.