The generator matrix
1 0 0 1 1 1
0 1 0 1 18 21
0 0 1 26 17 15
0 0 0 24 21 15
generates a code of length 6 over Z27 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+202x^6+48x^7+1998x^8+1212x^9+21510x^10+7992x^11+91500x^12+43020x^13+7992x^14+1604x^15+60x^16+8x^18
The gray image is a code over GF(3) with n=54, k=11 and d=18.
This code was found by Heurico 1.16 in 0.984 seconds.