The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+161x^44+168x^45+392x^46+452x^47+659x^48+576x^49+582x^50+408x^51+346x^52+184x^53+104x^54+4x^55+22x^56+22x^58+8x^60+4x^62+1x^64+1x^68+1x^72

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 0.391 seconds.