The generator matrix

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

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+253x^44+812x^45+1627x^46+2252x^47+2037x^48+2726x^49+2236x^50+1902x^51+1241x^52+728x^53+340x^54+112x^55+52x^56+38x^57+17x^58+6x^59+3x^62+1x^66

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 1.89 seconds.