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 2X+2 2X
generates a code of length 6 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+174x^2+1568x^3+9535x^4+43232x^5+153124x^6+43232x^7+9535x^8+1568x^9+174x^10+1x^12
The gray image is a code over GF(2) with n=48, k=18 and d=8.
This code was found by Heurico 1.16 in 8.63 seconds.