The generator matrix

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

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+58x^42+350x^43+642x^44+1110x^45+1561x^46+2044x^47+2086x^48+3298x^49+3281x^50+3808x^51+3178x^52+3406x^53+2641x^54+1942x^55+1260x^56+1080x^57+491x^58+294x^59+120x^60+56x^61+28x^62+10x^63+9x^64+10x^65+2x^66+2x^70

The gray image is a linear code over GF(2) with n=204, k=15 and d=84.
This code was found by Heurico 1.16 in 29.2 seconds.