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

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+53x^40+64x^41+145x^42+192x^43+287x^44+400x^45+471x^46+626x^47+707x^48+808x^49+780x^50+758x^51+757x^52+592x^53+409x^54+392x^55+298x^56+168x^57+95x^58+72x^59+59x^60+16x^61+15x^62+6x^63+12x^64+4x^66+2x^67+1x^68+1x^70+1x^72

The gray image is a linear code over GF(2) with n=200, k=13 and d=80.
This code was found by Heurico 1.16 in 3.9 seconds.