The generator matrix

 1  0  0  1  1  1  1  1  1
 0  1  0  1  a a+1 (a+1)X (a+1)X+1 (a+1)X+a
 0  0  1 a+1  a  1  1  0 a+1
 0  0  0  X  0  X  0 aX  X
 0  0  0  0  X (a+1)X (a+1)X  0 (a+1)X

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

Homogenous weight enumerator: w(x)=1x^0+51x^16+480x^18+135x^20+1152x^21+4320x^22+2514x^24+6912x^25+12960x^26+6144x^27+7230x^28+10368x^29+12960x^30+234x^32+75x^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 0.676 seconds.