The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 1 1 1 1 1 1 1 1 X X 2 0 2 0 2 2 2 2 2 X X 2X 2X X X 2
0 2X+2 0 2X+2 2X 2 2X 2 0 2X+2 0 2X+2 2X 2 2X 2 2X+2 2X+2 2 2 0 2X 0 2X 2X+2 2 0 2X 2X+2 2 0 2X 2X+2 2 2X+2 2 0 2X 2 2 2X 0 2X 2 2 0 2X 0
0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 0 2X 2X 2X 0 0 0 0
generates a code of length 48 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+117x^48+8x^52+2x^56
The gray image is a code over GF(2) with n=384, k=7 and d=192.
This code was found by Heurico 1.16 in 0.062 seconds.