The generator matrix
1 0 0 0 1 1
0 1 0 0 1 0
0 0 1 0 a^2 0
0 0 0 1 1 0
0 0 0 0 a^2*X X
generates a code of length 6 over F4[X]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+72x^6+45x^8+576x^9+864x^10+3768x^12+5184x^13+3888x^14+21504x^15+22203x^16+15552x^17+69216x^18+64512x^19+33192x^20+15552x^21+5832x^22+183x^24
The gray image is a linear code over GF(4) with n=24, k=9 and d=6.
This code was found by Heurico 1.16 in 3.17 seconds.