The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+284x^46+1310x^47+3797x^48+6128x^49+11091x^50+13698x^51+19898x^52+18538x^53+19961x^54+14276x^55+11306x^56+5516x^57+3249x^58+1310x^59+498x^60+122x^61+35x^62+26x^63+20x^64+4x^66+4x^67

The gray image is a linear code over GF(2) with n=424, k=17 and d=184.
This code was found by Heurico 1.16 in 109 seconds.