The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+114x^48+98x^49+267x^50+166x^51+610x^52+388x^53+883x^54+402x^55+568x^56+138x^57+242x^58+56x^59+100x^60+16x^61+12x^62+10x^63+13x^64+3x^66+6x^67+2x^68+1x^86

The gray image is a code over GF(2) with n=432, k=12 and d=192.
This code was found by Heurico 1.16 in 0.438 seconds.