The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3+X^2  1  1  1  1  1  0  1  X  1  0 X^3+X^2  1  1  X  X  1  1  1  X  1 X^3+X^2  1  1  X X^3+X^2  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^3+X^2+X X^3 X^3 X^3+X^2+X  X  X X^3+X^2+X  X X^2 X^2 X^3+X^2+X  X X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2  X X^2 X^3+X^2 X^2+X  X X^3 X^2+X X^3+X^2 X^3  0 X^3+X^2+X X^3+X  0  X  0
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  X X^3+X X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2 X^2+X  0 X^2+X  X X^2+X X^3+X^2+X X^3+X^2+X  0  X X^2 X^3 X^3+X  0  X  X X^3+X X^2+X X^3+X^2+X  X  0 X^3 X^3+X^2+X X^3 X^2+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^3 X^2  0 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 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+98x^45+227x^46+382x^47+477x^48+726x^49+500x^50+656x^51+367x^52+298x^53+132x^54+108x^55+48x^56+30x^57+28x^58+4x^59+10x^60+1x^62+2x^63+1x^76

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 0.313 seconds.