The generator matrix

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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+90x^45+178x^46+470x^47+356x^48+710x^49+487x^50+774x^51+334x^52+406x^53+163x^54+98x^55+10x^56+10x^57+2x^59+2x^60+2x^62+1x^64+1x^66+1x^70

The gray image is a linear code over GF(2) with n=400, k=12 and d=180.
This code was found by Heurico 1.16 in 97 seconds.