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  X  1  1 X^2 X^2  X  X X^2  0  1  1  1  X  X  1  1  0  0  1  1  X  X
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X  X  0  X  X X^2+X  X X^2  0 X^2 X^2  X  X  X X^2+X X^2+X X^2  X X^2 X^2  X  0  X  X X^2+X
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X  0 X^2 X^2  X  X  0  0 X^2+X  X X^2+X  0 X^2+X X^2+X X^2+X  X  0  X  0  X  X X^2 X^2  X
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X  0 X^2 X^2  0  X X^2 X^2  0 X^2+X X^2+X X^2+X  X X^2+X  X X^2+X  0  0 X^2+X  0  X  X X^2  X  0 X^2 X^2+X  X X^2+X  X
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  X  0  0  X X^2+X  X X^2  X  0 X^2 X^2+X  X X^2 X^2  0 X^2+X X^2 X^2 X^2+X X^2 X^2 X^2+X  0  X  0  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 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 42.

Homogenous weight enumerator: w(x)=1x^0+152x^42+4x^43+406x^44+56x^45+566x^46+148x^47+805x^48+496x^49+1156x^50+660x^51+1171x^52+440x^53+857x^54+204x^55+510x^56+32x^57+280x^58+8x^59+157x^60+56x^62+20x^64+4x^66+1x^68+1x^70+1x^76

The gray image is a linear code over GF(2) with n=204, k=13 and d=84.
This code was found by Heurico 1.16 in 4 seconds.