The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2 X^2+X  1  1 X^2+X X^2+X  1  1  1 X^2+X  1 X^2+X  1  1  0 X^2  X  0  1  1  1 X^2+X X^2+X  X  1  1  1  1  1  1  0  1  1  1  1  1  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1 X^2 X^2+X  1  1  1 X^2+1  0 X^2  1 X+1 X^2+X X^2+X  X X^2+X  1  1  0 X^2+X  X  X  1  1 X^2+X X+1  1  X X^2 X+1  1  1 X^2  X X^2  1  X  0
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1 X+1  0 X^2+1  X X^2+X+1 X+1 X^2  1 X^2+X+1 X^2+X  1  X X^2+1  1 X+1 X^2  X  1 X^2+X+1  1  X  1 X^2+X+1  X  1 X^2 X+1  X X^2  X X+1 X^2+X  0
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2 X+1 X^2+X  X X^2+X X^2+X+1  0 X^2+1 X^2+X X^2+1  0 X^2 X^2+1 X+1  0 X+1 X^2+X X^2+X X^2+1 X^2 X^2+1  0 X^2+1 X^2+X X^2+X+1 X+1  1 X+1  X  1  0  0  0
 0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 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  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 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+73x^42+336x^43+630x^44+1018x^45+1413x^46+2146x^47+2689x^48+2980x^49+3485x^50+3314x^51+3355x^52+3222x^53+2579x^54+2110x^55+1497x^56+898x^57+468x^58+278x^59+139x^60+72x^61+44x^62+8x^63+9x^64+2x^65+2x^66

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 29.6 seconds.