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

generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+80x^45+28x^46+78x^48+48x^49+160x^50+256x^51+160x^52+48x^53+56x^54+16x^56+80x^57+12x^62+1x^96

The gray image is a linear code over GF(2) with n=204, k=10 and d=90.
This code was found by Heurico 1.16 in 0.568 seconds.