The generator matrix
1 0 1 1 1 X
0 1 1 0 0 2
0 0 X 0 0 X
0 0 0 X 0 X
0 0 0 0 X X
0 0 0 0 0 2
generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+74x^2+64x^3+975x^4+1472x^5+3020x^6+1472x^7+975x^8+64x^9+74x^10+1x^12
The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0242 seconds.