The generator matrix

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

generates a code of length 48 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+153x^44+532x^45+624x^46+626x^47+494x^48+504x^49+542x^50+276x^51+179x^52+68x^53+48x^54+42x^55+5x^56+2x^66

The gray image is a code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 0.219 seconds.