The generator matrix
1 1 1 1 1 1 1 1 X 1 1 1
0 2 0 0 0 0 0 0 0 2 0 2
0 0 2 0 0 0 0 0 0 2 2 2
0 0 0 2 0 0 0 0 2 0 2 0
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^3+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+17x^6+38x^8+44x^10+128x^11+1588x^12+128x^13+54x^14+33x^16+12x^18+4x^20+1x^22
The gray image is a code over GF(2) with n=96, k=11 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.