The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+393x^44+104x^45+740x^46+480x^47+865x^48+272x^49+696x^50+160x^51+324x^52+8x^53+36x^54+6x^56+9x^60+2x^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 27.2 seconds.