The generator matrix

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

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+72x^48+60x^50+32x^51+190x^52+352x^53+700x^54+352x^55+128x^56+32x^57+52x^58+40x^60+20x^62+6x^64+10x^68+1x^96

The gray image is a code over GF(2) with n=432, k=11 and d=192.
This code was found by Heurico 1.16 in 0.234 seconds.