The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1 X^2  1  1  1 X^2+2  1  1  1  1  X  1  1  0  X  1  1  1  1  1  2  0 X^2  1  1  1  1 X^2+X+2  1  1 X+2  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1 X^2+1  2 X+2  1 X^2+1 X^2+X+2 X^2+X+3 X+1  1  1 X+1  1  1 X+3 X^2+1  1 X^2+X+3 X^2+X+3  1  1  1 X^2 X+2 X^2+2 X^2+X+2  1 X^2+2  X  1 X^2+X+3 X^2+3
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2+X+2 X^2+2 X^2+X X^2+X+2  0 X^2  2 X^2+X+2 X^2+X+2 X^2+X X^2 X^2+X  0  X X+2 X^2 X^2 X^2+X+2  X X^2+2  2 X^2 X+2  2  0 X+2  X X^2 X^2+2 X^2+X 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+150x^45+600x^46+230x^47+196x^48+186x^49+512x^50+110x^51+8x^52+16x^53+24x^54+12x^55+1x^60+1x^64+1x^68

The gray image is a code over GF(2) with n=384, k=11 and d=180.
This code was found by Heurico 1.16 in 0.094 seconds.