The generator matrix

 1  0  0  1  1  1  2  X 2X+2  1  1  1  2  1 2X+2 3X X+2  1  1  1  1 3X  1  X X+2  1  1 3X  1  1  1  1  1  1  1  1  1  2  1  2 2X+2  X  1  1  0  1  1  1
 0  1  0  0  3  3  1  X  1 2X  1 2X+1  1  2 3X+2 2X+2  1 X+3 X+2  X X+3  1 3X+2  1  1 3X 2X+3  1 3X+3 2X+1 3X+3  1 3X+1 2X  0 3X 2X  1 3X+1  2  1  1 2X+2 3X  1 X+1 2X+3 2X+2
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 2X+3 X+2  1  1  1  1 X+2 2X+3 2X+2  X 2X X+1  3 2X+2 2X+3 3X+3 3X+1 3X+3 2X+1  0 X+3  X 3X+2 X+2  1 2X+1 X+3 X+3 X+3  1  0 3X 2X+2  0  1 2X+3 X+3 3X+2
 0  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  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+307x^44+860x^45+1462x^46+956x^47+1554x^48+976x^49+892x^50+416x^51+390x^52+212x^53+98x^54+36x^55+27x^56+4x^58+1x^60

The gray image is a code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 0.5 seconds.