The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+304x^48+1666x^49+3676x^50+7018x^51+10088x^52+14554x^53+17645x^54+20528x^55+18422x^56+15030x^57+10279x^58+6480x^59+3066x^60+1626x^61+427x^62+146x^63+75x^64+18x^65+5x^66+2x^67+10x^68+2x^71+2x^72+2x^73

The gray image is a code over GF(2) with n=440, k=17 and d=192.
This code was found by Heurico 1.16 in 107 seconds.