The generator matrix
1 0 1 1 1 1
0 1 1 a 0 0
0 0 a^2*X 0 X 0
0 0 0 X a*X 0
generates a code of length 6 over F4[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+18x^8+48x^9+36x^12+144x^13+576x^15+57x^16+144x^17+768x^18+1728x^19+84x^20+432x^21+60x^24
The gray image is a linear code over GF(4) with n=24, k=6 and d=8.
This code was found by Heurico 1.16 in 0.00151 seconds.