The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+286x^47+1722x^48+3412x^49+6994x^50+9414x^51+15562x^52+17480x^53+21008x^54+17460x^55+16427x^56+9850x^57+6468x^58+2718x^59+1485x^60+476x^61+192x^62+66x^63+18x^64+14x^65+10x^66+8x^67+1x^68

The gray image is a linear code over GF(2) with n=432, k=17 and d=188.
This code was found by Heurico 1.16 in 108 seconds.