The generator matrix

 1  0  0  0  0  1  1  1  1  2  6  1  4  1  0  0  1  1  1  2  0  2  1  6  6  1  2
 0  1  0  0  0  0  4  0  0  4  1  7  1  7  1  1  6  6  3  2  1  0  5  1  1  3  1
 0  0  1  0  0  0  1  4  5  1  6  1  5  2  4  3  3  2  7  4  5  1  4  2  4  4  5
 0  0  0  1  0  1  1  2  0  7  2  0  2  7  7  3  2  1  1  1  2  5  6  1  3  3  6
 0  0  0  0  1  1  2  3  3  1  1  5  7  1  2  4  4  0  2  4  0  2  1  3  1  6  2
 0  0  0  0  0  4  0  0  4  4  4  4  4  0  4  4  4  4  4  0  0  4  4  4  0  4  4

generates a code of length 27 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+289x^20+760x^21+1836x^22+3224x^23+4920x^24+7216x^25+9184x^26+10120x^27+9540x^28+7800x^29+5040x^30+2888x^31+1653x^32+672x^33+256x^34+88x^35+43x^36+4x^38+2x^40

The gray image is a code over GF(2) with n=108, k=16 and d=40.
This code was found by Heurico 1.16 in 35.6 seconds.