The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+27x^24+48x^25+36x^26+78x^28+48x^29+12x^30+6x^32

The gray image is a linear code over GF(4) with n=36, k=4 and d=24.
This code was found by Heurico 1.16 in 3.24e-008 seconds.