The generator matrix

 1  0  1  1  1  1  1  3  3  3
 0  1  1 26  0 16 17  1  0 15
 0  0 24  0  9  6  6  3 24 21
 0  0  0  3 15 24 12 18 24  6

generates a code of length 10 over Z27 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+288x^14+720x^15+1296x^16+1728x^17+9456x^18+5184x^19+13176x^20+18792x^21+5184x^22+2304x^23+900x^24+20x^27

The gray image is a code over GF(3) with n=90, k=10 and d=42.
This code was found by Heurico 1.16 in 70.9 seconds.