The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  0  X
 0  0  X  0  0  0 (a+1)X  X (a+1)X
 0  0  0  X  0  0  X (a+1)X  0
 0  0  0  0  X  0 (a+1)X  X  0
 0  0  0  0  0  X aX  X  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+36x^12+174x^16+480x^20+912x^24+12288x^27+1284x^28+897x^32+312x^36

The gray image is a linear code over GF(4) with n=36, k=7 and d=12.
This code was found by Heurico 1.16 in 0.0641 seconds.