The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1 X^2  1  1  X  1 X^3  1 X^2  X  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3  0 X^3  0 X^3 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2 X^3  0 X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2  0 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2  0 X^3 X^3+X^2 X^3  0 X^2  0  0 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^3  0 X^3 X^3 X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  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+24x^44+56x^45+44x^46+154x^47+152x^48+448x^49+363x^50+428x^51+123x^52+148x^53+22x^54+20x^55+13x^56+16x^57+16x^58+4x^59+5x^60+4x^61+2x^62+2x^63+2x^64+1x^82

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 0.156 seconds.