The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+378x^46+192x^47+371x^48+128x^49+508x^50+192x^51+202x^52+70x^54+1x^60+4x^62+1x^76

The gray image is a code over GF(2) with n=392, k=11 and d=184.
This code was found by Heurico 1.16 in 22.8 seconds.