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

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

Homogenous weight enumerator: w(x)=1x^0+95x^44+146x^46+96x^47+161x^48+1088x^49+132x^50+96x^51+132x^52+74x^54+26x^56+1x^92

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 0.14 seconds.