The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+360x^45+828x^46+1374x^47+1199x^48+1354x^49+846x^50+966x^51+562x^52+362x^53+156x^54+108x^55+45x^56+20x^57+10x^58+1x^64

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 0.5 seconds.