The generator matrix

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

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+138x^44+8x^45+228x^46+64x^47+446x^48+184x^49+478x^50+272x^51+604x^52+248x^53+460x^54+160x^55+322x^56+72x^57+192x^58+16x^59+118x^60+48x^62+29x^64+2x^66+4x^68+2x^72

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 1 seconds.