The generator matrix

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

generates a code of length 9 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+192x^21+252x^24+1152x^25+648x^28+1728x^29+51x^32+24x^36

The gray image is a linear code over GF(4) with n=36, k=6 and d=20.
This code was found by Heurico 1.16 in 0.00633 seconds.