The generator matrix

 1  0  1  1  1  1  1  1  1
 0  1  1  a a^2  0 a^2*X+1  a  0
 0  0 a^2*X  0  0  X  0 a*X  X
 0  0  0  X  0 a^2*X a*X a^2*X a^2*X
 0  0  0  0 a^2*X  X  X a^2*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+51x^16+48x^18+135x^20+384x^21+432x^22+1746x^24+2304x^25+1296x^26+4926x^28+3456x^29+1296x^30+234x^32+75x^36

The gray image is a linear code over GF(4) with n=36, k=7 and d=16.
This code was found by Heurico 1.16 in 0.0507 seconds.