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  1  X  X  X  0  1  X  1  X  1  X  X  0  0  1  1  1 X^2  X  1  0 X^2 X^2  1  1  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X X^2  0  0 X^2 X^2+X X^2+X X^2 X^2+X  X  X X^2+X X^2 X^2 X^2+X X^2+X X^2  X  0  X X^2+X  X  0  X  0  X  X X^2  X X^2+X  X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2  0  0 X^2  X  X X^2  X  X X^2+X  X  0 X^2  X X^2  X  0 X^2  X  X X^2+X X^2  0  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2  X  0  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  0 X^2+X X^2+X  X  X  0  0  0 X^2+X  0  0  0  X  0 X^2  X X^2  X X^2  0  X  0  X  X  X  X X^2 X^2  X  X X^2+X X^2+X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  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 X^2 X^2  0  0  0 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 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  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+99x^44+16x^45+272x^46+128x^47+308x^48+392x^49+271x^50+456x^51+256x^52+608x^53+240x^54+272x^55+229x^56+136x^57+190x^58+40x^59+107x^60+40x^62+21x^64+11x^66+2x^68+1x^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 0.953 seconds.