The generator matrix

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

generates a code of length 20 over Z8 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+34x^14+132x^15+325x^16+568x^17+936x^18+1340x^19+1532x^20+1360x^21+908x^22+572x^23+306x^24+120x^25+40x^26+4x^27+12x^28+2x^30

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.376 seconds.