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 X X 1 X X 1 1 1
0 2X+2 0 2X+2 0 2X+2 0 2 2X 2X+2 0 2X+2 0 2X+2 2X 2 2 0 2X 2 0 2X 2X+2 2X+2 2X+2 2X+2 0 0 2X 2X 2X+2 2X+2 2 2 2X+2 2 2X+2 2 0 0 2X 2X 2X+2 0 0 2X+2 2X 0 2X
0 0 2X 0 0 0 0 0 2X 0 0 0 2X 0 2X 0 0 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 0 2X
0 0 0 2X 0 0 0 2X 0 0 0 2X 0 0 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 0 0 2X 0 2X 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 0
0 0 0 0 2X 0 0 0 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 0
0 0 0 0 0 2X 0 2X 0 2X 2X 0 2X 0 0 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 2X 2X
0 0 0 0 0 0 2X 0 2X 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 0 0 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 0 0 2X 2X 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+141x^44+40x^46+64x^47+81x^48+1408x^49+80x^50+64x^51+98x^52+8x^54+45x^56+17x^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 106 seconds.