The generator matrix
1 0 0 0 0 1 1 1 2 1 X+2 1
0 1 0 0 0 2 2 X+1 X+2 3 1 X
0 0 1 0 0 X+2 1 3 1 X+1 X+2 X
0 0 0 1 0 X+1 1 X+2 3 1 0 2
0 0 0 0 1 1 X X+1 1 X+2 X+1 0
generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 7.
Homogenous weight enumerator: w(x)=1x^0+146x^7+569x^8+1648x^9+3870x^10+6076x^11+7998x^12+6296x^13+3921x^14+1538x^15+520x^16+168x^17+16x^18+1x^22
The gray image is a code over GF(2) with n=48, k=15 and d=14.
This code was found by Heurico 1.13 in 0.849 seconds.