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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+25x^44+48x^45+87x^46+50x^47+293x^48+48x^49+1002x^50+14x^51+288x^52+52x^53+49x^54+30x^55+30x^56+8x^57+10x^58+2x^59+3x^60+4x^61+3x^62+1x^86

The gray image is a linear code over GF(2) with n=400, k=11 and d=176.
This code was found by Heurico 1.16 in 0.187 seconds.