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  0  0  X  X X^2  0  1  0  0  1  0 X^2  1  1 X^2  X  X
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  0  X  X X^2 X^2+X  X X^2+X X^2 X^2+X  X X^2 X^2  X  0  0  0 X^2+X  0  X X^2+X  X X^2  0  X  0  X X^2+X X^2 X^2+X X^2+X
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2+X  X X^2  X  X  X X^2  X  X  0  X X^2  0  X X^2  X X^2+X  X X^2  X X^2  X X^2  0 X^2 X^2+X X^2  X X^2  0
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2  X X^2+X X^2  X X^2+X  X  X X^2+X X^2  X  X  0  X X^2 X^2  0 X^2  0 X^2+X  X X^2 X^2  0  X  0  X X^2+X X^2+X X^2
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X X^2+X  X  0 X^2+X X^2+X X^2  0  0 X^2  X X^2 X^2+X  0 X^2 X^2  0  X  X X^2 X^2+X X^2  X  0 X^2 X^2 X^2 X^2 X^2  X X^2
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2+X  X  X X^2  0  0 X^2  X X^2 X^2+X  0 X^2  X  X X^2+X X^2  0  0 X^2 X^2+X X^2+X  0 X^2  0 X^2+X X^2 X^2 X^2  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+120x^42+416x^44+36x^45+636x^46+192x^47+810x^48+520x^49+1124x^50+596x^51+1121x^52+436x^53+840x^54+232x^55+533x^56+32x^57+322x^58+4x^59+142x^60+56x^62+16x^64+6x^66+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 4.04 seconds.