The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+40x^44+72x^45+151x^46+72x^47+373x^48+216x^49+616x^50+136x^51+747x^52+200x^53+619x^54+152x^55+335x^56+136x^57+131x^58+24x^59+28x^60+16x^61+11x^62+8x^64+4x^66+1x^68+3x^70+3x^72+1x^74

The gray image is a linear code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.714 seconds.