The generator matrix

 1  0  0  1  1  1  2  1  1 3X  1  2 2X  1  0  1  1  X  1  1 3X  1 3X+2  1 3X  1 3X 2X  1  1 3X  1  1  1  1 2X+2  1  1 X+2  1  1 3X  1  1  1 3X+2  1  1  1
 0  1  0  0  3  3  1 3X+1 3X 3X 2X+3  1  1 2X 3X+2  0 X+2  1 3X X+3  1 3X+2  1 2X+1  1 3X+3  2 X+2 3X+1 X+3  1 X+2 X+1 3X+3 X+3  1 2X+1 2X  1  0 3X X+2  1 2X+2 3X  1 X+3 3X 2X+2
 0  0  1 X+1 X+1 2X+2 3X+3 3X+1 X+2  1 3X  1 X+2 2X+1  1  X 3X+3  0 2X 2X+2 X+3  1 2X+3 X+1  X X+1  1  1  3 3X 2X+3 X+2 2X+3 2X+2 2X+1 2X+3  1 2X+2 2X+2 2X 3X+2  1 2X+3 2X+1 2X 2X 3X+2  0  2
 0  0  0 2X+2  2  0 2X+2  2 2X  2 2X  2  0 2X+2 2X  2  0  2 2X+2  2 2X 2X+2  0 2X  0 2X  2  2  0 2X+2 2X+2  2 2X+2  0 2X  0  0 2X 2X 2X+2 2X+2  0  2  2 2X 2X+2  2  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+255x^44+910x^45+1429x^46+2068x^47+2500x^48+2646x^49+2251x^50+1758x^51+1211x^52+750x^53+370x^54+134x^55+32x^56+46x^57+11x^58+6x^59+3x^62+2x^63+1x^64

The gray image is a code over GF(2) with n=392, k=14 and d=176.
This code was found by Heurico 1.16 in 1.98 seconds.