The generator matrix

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

Homogenous weight enumerator: w(x)=1x^0+33x^42+100x^43+146x^44+320x^45+355x^46+388x^47+742x^48+858x^49+727x^50+814x^51+1018x^52+822x^53+518x^54+398x^55+336x^56+266x^57+135x^58+86x^59+50x^60+34x^61+15x^62+6x^63+9x^64+4x^65+9x^66+2x^68

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 2.93 seconds.