The generator matrix

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

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+124x^44+104x^45+467x^46+378x^47+697x^48+586x^49+702x^50+380x^51+443x^52+72x^53+105x^54+10x^55+12x^56+2x^57+2x^58+4x^61+3x^62+2x^64+1x^68+1x^70

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 0.234 seconds.