The generator matrix
1 0 1 1 1 1
0 1 1 a a^2*X+a^2 0
0 0 a^2*X a*X X 0
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+60x^12+192x^15+21x^16+576x^19+156x^20+18x^24
The gray image is a linear code over GF(4) with n=24, k=5 and d=12.
This code was found by Heurico 1.16 in -1.01e-007 seconds.