The generator matrix

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

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+109x^44+258x^45+304x^46+438x^47+662x^48+692x^49+609x^50+428x^51+207x^52+190x^53+99x^54+30x^55+45x^56+8x^57+11x^58+4x^61+1x^78

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 0.297 seconds.