The generator matrix

 1  1  1  1  1  1
 0  X  0  0  X  0
 0  0  X  0 (a+1)X  0
 0  0  0  X  X  0

generates a code of length 6 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+18x^8+36x^12+57x^16+768x^18+84x^20+60x^24

The gray image is a linear code over GF(4) with n=24, k=5 and d=8.
This code was found by Heurico 1.16 in 3.24e-008 seconds.