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

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+562x^45+638x^46+860x^47+497x^48+564x^49+303x^50+332x^51+132x^52+134x^53+24x^54+40x^55+2x^56+4x^57+3x^58

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 107 seconds.