The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  X a^2*X a^2*X  0  X a*X
 0  0  X a^2*X a^2*X  X a*X a*X 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+30x^24+192x^27+18x^28+9x^32+6x^36

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 -6.87e-008 seconds.