The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  X  1  1  1  1  1  0  1  2  1  1 X+2 X^2+X+2  1  0 X+2 X^2 X^2+2  1  1  1  1 X^2+X  1  1 X+2  1 X^2+2  1  1 X^2+2  1 X+2  1  1 X^2+2  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3 X^2+2  1  X  1  3 X^2+X+1  1 X+1  0  1  2  1 X+1 X^2+X  1  1 X^2+X+2  1  1  1  1 X^2+3 X^2  3 X+3  1 X+1 X^2+X+3  1 X+2  1 X^2+X+2 X+2  1 X^2+X+1  1 X^2+X+2 X^2+1  1  2 X^2+3
 0  0 X^2  0  0  0  0  2  2  2  2  2 X^2  2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2+2  2  2  2 X^2 X^2  2 X^2+2  2 X^2+2  2  0 X^2+2 X^2 X^2+2 X^2  2 X^2  2  2  2  2 X^2+2  2  2
 0  0  0 X^2+2  2 X^2+2 X^2  2  2 X^2 X^2  0  2 X^2+2 X^2 X^2+2 X^2+2  2  2 X^2+2 X^2+2 X^2  2  0 X^2+2  2 X^2  0  2 X^2+2 X^2 X^2 X^2+2  0 X^2  2 X^2 X^2+2  0  2 X^2+2 X^2  0  0  2 X^2  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+280x^44+272x^45+660x^46+496x^47+713x^48+496x^49+648x^50+272x^51+232x^52+4x^54+9x^56+11x^60+1x^64+1x^68

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 3.45 seconds.