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

generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+62x^40+92x^41+195x^42+268x^43+348x^44+412x^45+536x^46+774x^47+1096x^48+1540x^49+1874x^50+2008x^51+1865x^52+1552x^53+1085x^54+828x^55+549x^56+412x^57+314x^58+172x^59+157x^60+84x^61+87x^62+46x^63+16x^64+4x^65+4x^66+2x^68+1x^82

The gray image is a linear code over GF(2) with n=204, k=14 and d=80.
This code was found by Heurico 1.16 in 14.8 seconds.