The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+524x^45+686x^46+760x^47+718x^48+436x^49+352x^50+252x^51+140x^52+144x^53+18x^54+60x^55+4x^56+1x^64

The gray image is a code over GF(2) with n=384, k=12 and d=180.
This code was found by Heurico 1.16 in 2.09 seconds.