The generator matrix

 1  0  0  1  1  1  X  1 X^2  1 X^2+X X^2  1  1  1 X^3+X  1 X^3+X^2+X X^2  1  1  1 X^3+X^2+X X^3+X  1  1 X^3+X^2  0  1  X  X X^3 X^3+X^2+X  1  1  1 X^3+X  1  1  1  1  1  1  0 X^3 X^2  1  1  1  1
 0  1  0  0 X^2+1 X^2+X+1  1 X^2+X  1 X^3+1  1 X^3+X X^3+1 X^2  0  1  X  1  X X^3+X^2+1 X^3+X^2+1 X^3+X^2+X+1  1  X X^3+X^2+X X^2+1  1  1 X^2+X+1 X^3+X^2  1  1  1 X^2+X+1  0 X^2+1 X^3 X^3 X^3+X^2 X^3+X^2+X+1 X^3+1  0  1  1  1  1  1 X^3+X^2+X+1 X^3+X+1  0
 0  0  1  1  1  0 X^2+X+1 X^3+1 X^3 X^2+1 X^2+X+1  1 X^2+X X^2  1 X^3+1 X^2 X^2  1 X^3+X+1  X X^3+X+1 X^3+X^2  1 X^3+X^2+X+1 X^3 X+1 X^3+X^2+X X^3+X^2+X+1  1 X^2+X  1 X^2+X+1 X^3+1 X^2+X+1 X^3+X  1 X^2 X^3 X^2+X X^3+1 X^2+X  X X^3 X^2+X+1 X^3+1  X X^3+X^2 X^2+X  0
 0  0  0  X X^3+X X^3+X X^2+X  X X^3+X X^3 X^3 X^3+X^2+X X^3+X^2 X^2+X X^2 X^2+X X^3+X^2+X X^3+X  0 X^2+X X^3+X^2+X  0 X^3+X^2  X X^3+X^2 X^2 X^3+X^2 X^3+X X^2+X  0 X^3 X^3+X^2  X X^3+X^2 X^2  0 X^3+X^2+X  0 X^3+X X^3+X X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2+X X^2+X X^3  0 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+179x^44+808x^45+1704x^46+2648x^47+3813x^48+4702x^49+5157x^50+4866x^51+3721x^52+2656x^53+1471x^54+564x^55+269x^56+118x^57+45x^58+18x^59+16x^60+4x^61+5x^62+1x^64+2x^66

The gray image is a linear code over GF(2) with n=400, k=15 and d=176.
This code was found by Heurico 1.16 in 9.84 seconds.