The generator matrix

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

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+80x^45+237x^46+212x^47+362x^48+312x^49+315x^50+228x^51+207x^52+52x^53+23x^54+8x^55+5x^56+4x^57+1x^60+1x^74

The gray image is a code over GF(2) with n=392, k=11 and d=180.
This code was found by Heurico 1.16 in 0.094 seconds.