The generator matrix
1 1 1 1 1 1
0 X 0 X 0 0
0 0 X X 0 0
0 0 0 2 0 0
0 0 0 0 2 0
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+18x^2+111x^4+764x^6+111x^8+18x^10+1x^12
The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000523 seconds.