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  0 X^2  X  X  X  X X^2  X  0  1  X X^2  1  1 X^2  X X^2  X  1  X  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2 X^2 X^2+X  0 X^2 X^2+X  X X^2+X  X  X X^2+X  0  X  X X^2 X^2  0 X^2 X^2+X  0  X  X  X X^2  0  0  0  X  X  X  0  X  X  0
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X  X X^2+X X^2 X^2+X  0 X^2 X^2+X  X X^2  X  0 X^2  X  X  X  0 X^2+X  X X^2+X  X X^2  X X^2  X  X  0 X^2  X X^2+X X^2  X  X  0  0
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X  0 X^2+X X^2+X  X X^2+X  X X^2  X X^2 X^2 X^2  X  0  0  0  0  X  0  0 X^2 X^2  X X^2 X^2+X  X  0 X^2 X^2+X X^2+X X^2+X X^2 X^2  X  0
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  X  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X  0  X  0  X X^2+X  X  X X^2+X  0 X^2+X X^2+X  X  0  X  X X^2  0  0 X^2+X X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  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+69x^40+86x^41+208x^42+258x^43+336x^44+582x^45+743x^46+882x^47+1119x^48+1384x^49+1618x^50+1730x^51+1689x^52+1460x^53+1108x^54+984x^55+685x^56+510x^57+326x^58+218x^59+164x^60+70x^61+81x^62+22x^63+30x^64+4x^65+8x^66+2x^67+3x^68+4x^70

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.