The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+412x^45+794x^46+1252x^47+1266x^48+1440x^49+923x^50+824x^51+471x^52+412x^53+229x^54+132x^55+21x^56+8x^57+5x^58+1x^60+1x^62

The gray image is a code over GF(2) with n=392, k=13 and d=180.
This code was found by Heurico 1.16 in 0.516 seconds.