The generator matrix

 1  0  0  1  1  1
 0  1  0  1  a  X
 0  0  1 a^2  a a*X

generates a code of length 6 over F4[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+132x^12+96x^13+192x^15+453x^16+384x^17+1152x^18+576x^19+804x^20+288x^21+18x^24

The gray image is a linear code over GF(4) with n=24, k=6 and d=12.
This code was found by Heurico 1.16 in 1.01e-007 seconds.