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  1  1  1  1  1  X  1  1  1  1  1  0  1  1  1  1  X  1  1  0  1  1  1 2X
 0  X  0 3X+2 2X X+2  0  X  2 3X+2  2 3X  2 3X+2 2X+2  X  0 X+2 2X+2 3X+2 3X+2  X 2X 2X  0  2 X+2  X 3X  2 X+2  X  2 3X  0  2  X  2 3X  X  0 3X+2 3X+2 2X+2 2X 2X  0  0  X
 0  0 2X+2  0  0 2X+2  2  2  2  2  2  2 2X  0  0 2X  0 2X  0 2X+2  2  0  2 2X+2 2X 2X 2X+2 2X  0  2 2X 2X+2  0 2X+2 2X 2X+2  0  2  2 2X+2 2X  0 2X 2X+2  2 2X  0  2  2
 0  0  0 2X+2  2 2X+2  2  0  0 2X  2  2  0 2X  2  2 2X 2X 2X+2  0  2  2 2X+2 2X  0 2X+2  2 2X 2X+2 2X  0  2  0 2X 2X+2  0  0 2X+2 2X 2X+2 2X 2X+2  0 2X+2 2X  2  2  0 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+180x^45+63x^46+196x^47+470x^48+290x^49+420x^50+212x^51+54x^52+100x^53+11x^54+40x^55+2x^56+6x^57+2x^58+1x^88

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 141 seconds.