The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  0  1  1  1 X^2+X  1  1 X^2+X  1  1  1  0  1  X  1  0  1  1 X^2  1  1  1  1  0  X  1  1  1  1  1  1  1 X^2+X X^2+X  1  1 X^2  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0  1 X+1 X^2+X X^2+1  1  0 X^2+1  1 X^2+X  0 X^2+1  1 X+1  1 X+1  1 X^2+X X^2+X+1  1 X^2  X X^2+1 X^2+X+1  1  0 X^2+1 X^2+X X^2 X^2+X X^2  X X+1  1  1 X^2+X+1 X^2  0  0
 0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 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 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 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+24x^44+74x^45+78x^46+224x^47+70x^48+324x^49+86x^50+336x^51+93x^52+288x^53+70x^54+192x^55+56x^56+76x^57+16x^58+16x^59+10x^60+6x^61+2x^62+1x^64+2x^66+1x^68+2x^70

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 0.207 seconds.