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 X^2  1 X^2  1  1  1  1  1  X  1  1  1  0  1  0  0  1  1  X  X X^2  1  1  X  1  1  1  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X  X  X X^2 X^2+X  X X^2+X X^2 X^2  0 X^2  X  X X^2+X  X  X X^2+X X^2  X  0  0  X X^2+X  0  X X^2+X X^2+X  0
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X X^2+X  0 X^2 X^2+X  X  0 X^2+X  X X^2+X X^2 X^2+X  0 X^2+X X^2+X  0  0 X^2+X  X X^2 X^2  0 X^2  0 X^2+X X^2+X X^2  0  X
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X  0 X^2+X X^2+X  0  X  0  0 X^2 X^2+X X^2 X^2 X^2  X  X X^2  X X^2 X^2 X^2+X X^2+X  X X^2  0 X^2  X X^2+X X^2  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  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 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  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+47x^44+68x^45+104x^46+144x^47+168x^48+196x^49+212x^50+248x^51+214x^52+198x^53+149x^54+94x^55+52x^56+36x^57+39x^58+20x^59+19x^60+10x^61+7x^62+6x^63+11x^64+4x^65+1x^82

The gray image is a linear code over GF(2) with n=204, k=11 and d=88.
This code was found by Heurico 1.16 in 0.28 seconds.