The generator matrix
1 1 1 1 X 0 1 1 X 1 1 1
0 X 0 X+2 X X 0 X+2 X+2 0 0 X+2
0 0 2 0 0 0 0 0 0 2 0 2
0 0 0 2 0 0 0 0 2 2 0 2
0 0 0 0 2 0 0 0 2 0 0 2
0 0 0 0 0 2 0 0 2 0 2 2
0 0 0 0 0 0 2 0 2 2 2 0
0 0 0 0 0 0 0 2 2 2 0 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+17x^6+8x^7+54x^8+72x^9+236x^10+432x^11+404x^12+432x^13+246x^14+72x^15+49x^16+8x^17+12x^18+4x^20+1x^22
The gray image is a code over GF(2) with n=48, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00734 seconds.