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.