The generator matrix

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

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+156x^45+130x^46+264x^47+252x^48+508x^49+270x^50+196x^51+96x^52+100x^53+14x^54+48x^55+2x^56+4x^57+2x^58+4x^59+1x^80

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 115 seconds.