The generator matrix

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

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+48x^20+192x^21+252x^24+1152x^25+648x^28+1728x^29+51x^32+24x^36

The gray image is a linear code over GF(4) with n=36, k=6 and d=20.
This code was found by Heurico 1.16 in 0.00635 seconds.