The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+162x^48+860x^49+1923x^50+2752x^51+3864x^52+4654x^53+5032x^54+4286x^55+3654x^56+2694x^57+1537x^58+726x^59+396x^60+106x^61+59x^62+42x^63+3x^64+6x^65+8x^66+2x^67+1x^70

The gray image is a code over GF(2) with n=432, k=15 and d=192.
This code was found by Heurico 1.16 in 8.23 seconds.