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

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+74x^45+92x^46+218x^47+268x^48+212x^49+81x^50+68x^51+2x^52+2x^53+2x^54+2x^55+1x^56+1x^90

The gray image is a code over GF(2) with n=384, k=10 and d=180.
This code was found by Heurico 1.16 in 0.109 seconds.