The generator matrix
1 0 0 1 1 1 15 15 1 1
0 1 0 1 15 26 1 1 18 18
0 0 1 26 16 26 22 19 20 18
0 0 0 24 15 9 3 15 6 21
generates a code of length 10 over Z27 who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+60x^13+510x^14+358x^15+4092x^16+3060x^17+23670x^18+15768x^19+61848x^20+47168x^21+15888x^22+4080x^23+482x^24+156x^25+2x^27+4x^30
The gray image is a code over GF(3) with n=90, k=11 and d=39.
This code was found by Heurico 1.16 in 4.47 seconds.