The generator matrix

 1  0  1  1  1  1  1  1  1
 0  1 (a+1)X+1  a (a+1)X+a+1  X aX+1 X+a 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+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 6.87e-008 seconds.