The generator matrix

 1  0  0  1  1  1  1  1  0  1
 0  1  0 15  1 16 26 20  1  0
 0  0  1 25  1 14 24 17 26  0
 0  0  0 18  9 18  9  0  9  9

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

Homogenous weight enumerator: w(x)=1x^0+210x^14+94x^15+1566x^16+1260x^17+5884x^18+6264x^19+24066x^20+11608x^21+6264x^22+1680x^23+140x^24+10x^27+2x^30

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 0.551 seconds.