The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  7 26 21  4 24  0 26  0
 0  0  9  0  0  9  0  9  9 18
 0  0  0  9  0 18 18 18  0 18
 0  0  0  0 18  9 18 18  9  9

generates a code of length 10 over Z27 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+30x^13+54x^14+72x^15+330x^16+324x^17+2652x^18+1260x^19+7938x^20+5184x^21+1230x^22+432x^23+90x^24+66x^25+20x^27

The gray image is a code over GF(3) with n=90, k=9 and d=39.
This code was found by Heurico 1.16 in 0.18 seconds.