The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+57x^44+240x^45+314x^46+516x^47+592x^48+664x^49+599x^50+544x^51+301x^52+184x^53+41x^54+28x^55+6x^56+3x^58+1x^60+1x^62+1x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.218 seconds.