The generator matrix
1 0 0 1 1 1
0 1 0 1 2 1
0 0 1 1 X 1
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+88x^3+583x^4+2984x^5+9072x^6+2984x^7+583x^8+88x^9+1x^12
The gray image is a code over GF(2) with n=48, k=14 and d=12.
This code was found by Heurico 1.16 in 0.063 seconds.