The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  0  X  1  1  1 X^2+X  X  1  1  X  1 X^2  0  1  1  1  1  1  1  X X^2+X  0 X^2+X  1  1 X^2  1  1  1  1  1  1  X  1  1  0 X^2+X  1  1  1  1
 0  1  0  0  1  1  1 X^2  0  X  1  1 X^2+X+1 X^2+X X+1  1  1  X X+1 X^2+X  X  1  0  1 X^2+1 X^2 X^2+X+1 X^2  X  1  1  1  X  1 X+1  1 X^2 X^2+X+1  X X^2+X+1  1 X^2  1 X^2+1 X^2+X+1  1  1 X^2+1 X^2+X+1 X^2+1 X^2
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+1  1 X^2+X  1  X X+1 X+1 X+1  0  X X^2  1 X^2+X+1 X^2+1  1  1 X^2+X  1 X+1 X^2 X^2+1 X^2+X  0 X+1  1 X^2+1  0 X^2  X X^2 X^2+1  X X+1  1  1  0 X^2+X X^2+X+1 X^2+1 X^2+1 X^2  0  X
 0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 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 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 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+174x^44+172x^45+555x^46+468x^47+829x^48+624x^49+1058x^50+616x^51+1055x^52+576x^53+754x^54+408x^55+436x^56+160x^57+172x^58+40x^59+50x^60+4x^61+19x^62+4x^63+14x^64+2x^66+1x^68

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 2.61 seconds.