The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+42x^20+84x^24+768x^27+36x^28+75x^32+18x^36

The gray image is a linear code over GF(4) with n=36, k=5 and d=20.
This code was found by Heurico 1.16 in -1.01e-007 seconds.