The generator matrix

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

generates a code of length 9 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+45x^16+48x^18+153x^20+384x^21+432x^22+1734x^24+2304x^25+1296x^26+4914x^28+3456x^29+1296x^30+252x^32+69x^36

The gray image is a linear code over GF(4) with n=36, k=7 and d=16.
This code was found by Heurico 1.16 in 0.0516 seconds.