The generator matrix

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

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+205x^48+948x^49+1810x^50+2836x^51+3483x^52+4954x^53+4646x^54+4830x^55+3506x^56+2760x^57+1386x^58+812x^59+374x^60+118x^61+50x^62+18x^63+22x^64+4x^65+4x^66+1x^76

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 7.67 seconds.