The generator matrix

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

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+260x^45+811x^46+1766x^47+1716x^48+2848x^49+2292x^50+2364x^51+1579x^52+1522x^53+586x^54+366x^55+137x^56+68x^57+36x^58+16x^59+5x^60+6x^61+3x^62+2x^64

The gray image is a linear code over GF(2) with n=400, k=14 and d=180.
This code was found by Heurico 1.16 in 7.81 seconds.