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.