The generator matrix

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

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+87x^44+284x^45+505x^46+570x^47+680x^48+804x^49+880x^50+912x^51+701x^52+734x^53+708x^54+470x^55+309x^56+208x^57+164x^58+84x^59+44x^60+18x^61+15x^62+12x^63+2x^64

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 2.58 seconds.