The generator matrix

 1  1  1  1  1  1
 0  X  0  0  0  X
 0  0  X  0  0 a^2*X
 0  0  0  X  0  X
 0  0  0  0  X a^2*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+120x^12+315x^16+3072x^18+360x^20+183x^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 0.00281 seconds.