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

generates a code of length 49 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+152x^44+80x^46+64x^47+575x^48+384x^49+432x^50+64x^51+230x^52+63x^56+2x^60+1x^88

The gray image is a code over GF(2) with n=392, k=11 and d=176.
This code was found by Heurico 1.16 in 16.9 seconds.