The generator matrix

 1  0  0  1  1  1
 0  1  0  1 a^2*X  0
 0  0  1 a^2  1  0
 0  0  0  X a^2*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+6x^8+24x^9+48x^10+372x^12+216x^13+144x^14+1152x^15+2097x^16+648x^17+4176x^18+3456x^19+3108x^20+648x^21+240x^22+48x^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 0.015 seconds.