The generator matrix

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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+489x^48+2120x^49+3564x^50+5428x^51+7284x^52+8972x^53+9910x^54+9108x^55+7444x^56+5484x^57+3152x^58+1600x^59+556x^60+276x^61+88x^62+20x^63+14x^64+12x^65+4x^66+4x^67+4x^68+2x^70

The gray image is a code over GF(2) with n=432, k=16 and d=192.
This code was found by Heurico 1.16 in 29.8 seconds.