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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+240x^46+32x^47+222x^48+224x^49+618x^50+224x^51+223x^52+32x^53+220x^54+10x^58+1x^60+1x^88

The gray image is a linear code over GF(2) with n=400, k=11 and d=184.
This code was found by Heurico 1.16 in 27.3 seconds.