The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0 a*X  X
 0  0  X  0  0 a^2*X  X  0 a^2*X
 0  0  0  X  0  X a^2*X a^2*X  0
 0  0  0  0  X a^2*X a*X  X  X

generates a code of length 9 over F4[X]/(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 0.00757 seconds.