The generator matrix
1 1 X 1 1 1
0 X^2+2 X^2+2 0 0 2
0 0 2 0 2 2
0 0 0 2 2 0
generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+12x^4+32x^5+166x^6+32x^7+11x^8+2x^10
The gray image is a code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.