The generator matrix

 1  0  1  1  1  1
 0  1  1  a  0  0
 0  0 (a+1)X  0  X  0
 0  0  0  X aX  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+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.