The generator matrix

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

generates a code of length 55 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+346x^48+1670x^49+3775x^50+6232x^51+10910x^52+14478x^53+18394x^54+18846x^55+19146x^56+14938x^57+10904x^58+6054x^59+3286x^60+1254x^61+486x^62+226x^63+53x^64+40x^65+25x^66+2x^67+4x^69+2x^72

The gray image is a linear code over GF(2) with n=440, k=17 and d=192.
This code was found by Heurico 1.16 in 121 seconds.