The generator matrix

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

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+72x^16+432x^18+90x^20+1152x^21+4464x^22+2532x^24+6912x^25+12816x^26+6144x^27+7236x^28+10368x^29+13008x^30+243x^32+66x^36

The gray image is a linear code over GF(4) with n=36, k=8 and d=16.
This code was found by Heurico 1.16 in 0.693 seconds.