The generator matrix
1 1 1 1 1 1
0 2 0 0 2X 2
0 0 2 0 2 2
0 0 0 2 2X+2 2X
generates a code of length 6 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+16x^3+39x^4+48x^5+816x^6+48x^7+39x^8+16x^9+1x^12
The gray image is a code over GF(2) with n=48, k=10 and d=12.
This code was found by Heurico 1.16 in 3.62e-008 seconds.