The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1  X X^3+X^2+X  1  1  1  1  X X^3  1 X^3  1 X^3+X^2+X X^2+X X^3+X^2  1  1 X^2 X^2 X^3+X^2+X  1 X^2+X  1  1  1  1  1  1 X^2+X X^3+X^2  1  1  1 X^2+X X^3  1  1  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^2+1  1  1 X+1 X^3+X^2+1  X X^3+X^2+X+1  1 X^3+X X^3 X^2+X X^2+X+1  1  1  1 X^3+X^2+X  X  1 X^2  1 X^3+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^2+X X^2 X^3+X  1 X^3  1 X^3+X^2  X X^3+1  1  1 X^2+X X^2 X^3
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1  X X^2 X^3+X^2+X+1 X^3+X^2+X X^3+X+1 X^2+X+1  1 X^3+X^2+1  1  0 X^2  X  1 X^2 X^3+X  1 X^3+X X^3+X^2+X+1  1 X^2+1 X^2+X+1  1 X^2+1 X^2+X X^2+X X^3+X^2+1 X^2+X+1  0 X^3+X^2+X X^3 X^3  X X^3 X^3+X+1 X^3+1 X^3+X X^3+1  0
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2 X^3+X^2+1 X^3+X^2 X^3+1 X^3+X^2+X+1 X^3+X^2+X X^2+X X^2+X X^3+X^2 X^2+X+1  1 X^3+X^2 X^2+1 X^3+X^2+X X^3+X^2+1 X^2+1 X+1 X^3+1 X^2+1 X^2 X^3+X^2+X+1  X X^3+X^2 X+1 X^2 X^3+X^2+X+1 X^3+X X^2+1  1  0  X X^3+1 X^3+X^2+X X^2 X^3+1 X^3+X^2+X  1  0
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3 X^2 X^3+X^2 X^3 X^2 X^2 X^3  0  0 X^3+X^2

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+133x^42+884x^43+2592x^44+6044x^45+11531x^46+19856x^47+29802x^48+38574x^49+42211x^50+39586x^51+30392x^52+20286x^53+11330x^54+5302x^55+2195x^56+960x^57+322x^58+82x^59+38x^60+2x^61+9x^62+2x^63+4x^64+6x^65

The gray image is a linear code over GF(2) with n=400, k=18 and d=168.
This code was found by Heurico 1.16 in 380 seconds.