The generator matrix
1 1 1 1 1 1 1 1 X X 1 1
0 X 0 0 0 X X+2 X 2 2 0 0
0 0 X 0 X X X+2 0 0 0 X+2 X
0 0 0 X X 0 X+2 X X X X+2 X
0 0 0 0 2 0 0 0 0 2 2 2
0 0 0 0 0 2 0 0 2 0 2 2
0 0 0 0 0 0 2 0 2 0 2 0
0 0 0 0 0 0 0 2 2 2 2 0
generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+79x^6+348x^8+1450x^10+4426x^12+1472x^14+339x^16+70x^18+6x^20+1x^22
The gray image is a code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 1.04 seconds.