The generator matrix
1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 aX X
0 0 X 0 0 (a+1)X X 0 (a+1)X
0 0 0 X 0 X (a+1)X (a+1)X 0
0 0 0 0 X (a+1)X aX X 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+153x^20+198x^24+3072x^27+306x^28+252x^32+69x^36
The gray image is a linear code over GF(4) with n=36, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00755 seconds.