The generator matrix

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

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+80x^44+342x^45+465x^46+586x^47+663x^48+772x^49+859x^50+800x^51+861x^52+764x^53+686x^54+450x^55+319x^56+280x^57+122x^58+70x^59+23x^60+14x^61+9x^62+12x^63+5x^64+4x^65+3x^66+2x^67

The gray image is a linear code over GF(2) with n=204, k=13 and d=88.
This code was found by Heurico 1.16 in 2.63 seconds.