The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+330x^16+1548x^20+16488x^24+42996x^28+3789x^32+324x^36

The gray image is a linear code over GF(4) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.5 seconds.