The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  X (a+1)X (a+1)X  0  X aX
 0  0  X (a+1)X (a+1)X  X aX aX aX

generates a code of length 9 over F4[X,sigma]/(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 3.24e-008 seconds.