The generator matrix
1 0 0 0 1 1
0 1 0 0 X+1 0
0 0 1 0 1 0
0 0 0 1 1 0
0 0 0 0 2 0
generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+172x^2+1456x^3+7175x^4+20944x^5+71576x^6+20944x^7+7175x^8+1456x^9+172x^10+1x^12
The gray image is a code over GF(2) with n=48, k=17 and d=8.
This code was found by Heurico 1.16 in 1.97 seconds.