The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+84x^18+96x^19+45x^20+336x^21+756x^22+288x^23+456x^24+2016x^25+2268x^26+2976x^27+1206x^28+3024x^29+2268x^30+480x^31+63x^32+21x^36

The gray image is a linear code over GF(4) with n=36, k=7 and d=18.
This code was found by Heurico 1.16 in 0.062 seconds.