The generator matrix

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

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+90x^44+238x^45+286x^46+616x^47+551x^48+750x^49+550x^50+442x^51+184x^52+150x^53+70x^54+88x^55+52x^56+14x^57+6x^58+6x^59+1x^60+1x^76

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 0.281 seconds.