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  1  1  1  1  0  1  X X^2  1  X  1  X  1  0  1  0 X^2  X  X  1  1  X  0  X  X
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2+X X^2  X  X  X  0 X^2+X  X X^2+X X^2  X X^2  X  0  X X^2  0 X^2+X  X X^2  0 X^2 X^2+X  X  X X^2+X  X  X X^2 X^2  X  X X^2+X X^2 X^2+X X^2+X  X  0 X^2+X
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0 X^2+X X^2 X^2 X^2 X^2  X X^2+X  X  0  X X^2+X X^2 X^2+X  0  0 X^2+X  X  X  0  0 X^2  X X^2+X X^2+X X^2+X X^2 X^2  X X^2+X  0  X X^2 X^2+X X^2+X  X X^2  X X^2+X  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2+X  0  X X^2 X^2+X  X X^2+X  X  X X^2 X^2  X X^2+X  X X^2 X^2 X^2+X X^2  X X^2+X  X X^2 X^2 X^2+X X^2  X  X  0 X^2  X X^2+X X^2+X X^2+X  0  X  0 X^2+X  X X^2
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0  0  X  X X^2+X  0 X^2  X  0  X X^2 X^2 X^2+X X^2+X X^2  0  X X^2+X  X X^2+X  X  0  X  X X^2+X  X X^2+X X^2 X^2+X X^2  X  X X^2  X  0  0  0  0  X  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  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+71x^44+126x^45+146x^46+182x^47+272x^48+320x^49+375x^50+420x^51+361x^52+436x^53+343x^54+286x^55+249x^56+152x^57+133x^58+50x^59+67x^60+46x^61+27x^62+20x^63+2x^64+8x^65+2x^67+1x^76

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 0.937 seconds.