The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+246x^47+1619x^48+3692x^49+6438x^50+10270x^51+15351x^52+17778x^53+19798x^54+18654x^55+15314x^56+10320x^57+6539x^58+2956x^59+1321x^60+508x^61+150x^62+80x^63+24x^64+4x^65+1x^66+2x^67+2x^68+2x^69+2x^70

The gray image is a code over GF(2) with n=432, k=17 and d=188.
This code was found by Heurico 1.16 in 113 seconds.