The generator matrix

 1  0  1  1  1  1
 0  1  1  a  0  0
 0  0 a^2*X  0  0  X
 0  0  0  X  0 a^2*X
 0  0  0  0  X  X

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+45x^8+48x^9+120x^12+432x^13+2304x^15+315x^16+1296x^17+3072x^18+6912x^19+360x^20+1296x^21+183x^24

The gray image is a linear code over GF(4) with n=24, k=7 and d=8.
This code was found by Heurico 1.16 in 0.0226 seconds.