The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+432x^22+468x^24+864x^26+1296x^28+1008x^30+27x^32

The gray image is a linear code over GF(4) with n=36, k=6 and d=22.
This code was found by Heurico 1.16 in 0.094 seconds.