The generator matrix
1 1 1 1 1 1 1 1 X 2 1 1
0 X 0 0 0 0 0 X 0 2 X+2 X+2
0 0 X 0 0 0 0 X X+2 X X X
0 0 0 X 0 0 0 X X+2 X+2 2 0
0 0 0 0 X 0 X X 2 X 2 2
0 0 0 0 0 X X 2 X X X+2 X+2
0 0 0 0 0 0 2 2 0 2 2 2
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+154x^6+724x^8+2346x^10+2048x^11+5826x^12+2048x^13+2366x^14+731x^16+126x^18+14x^20
The gray image is a code over GF(2) with n=48, k=14 and d=12.
This code was found by Heurico 1.16 in 6.77 seconds.