The generator matrix

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

generates a code of length 9 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+51x^12+348x^16+1545x^20+16500x^24+42933x^28+3855x^32+303x^36

The gray image is a linear code over GF(4) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.499 seconds.