The generator matrix

 1  1  1  1  1  1  1  1  1  2  2  2  1  1  1  0  4  0  1  2  1  4  1  1  1  0  1  2  1  2  1
 0  2  0  2  0  0  2  6  0  0  2  6  4  6  6  0  2  2  6  2  4  2  2  0  0  2  4  4  2  4  0
 0  0  2  2  0  6  2  0  0  2  2  4  2  6  0  2  6  0  0  2  2  6  2  0  0  0  4  2  4  2  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  4  0  0  4  4  0  0  4  0  0  4  0  4  4  4  4  0  0
 0  0  0  0  4  0  0  0  0  0  0  4  4  0  0  0  4  0  0  4  0  4  0  4  0  4  0  4  0  0  4
 0  0  0  0  0  4  0  0  0  0  0  0  4  0  4  4  0  4  0  0  4  4  4  0  4  0  4  0  0  4  4
 0  0  0  0  0  0  4  0  0  0  0  0  4  4  0  4  4  0  4  0  4  4  0  0  4  4  0  4  0  4  0
 0  0  0  0  0  0  0  4  0  0  0  0  0  4  4  0  0  4  0  4  4  0  4  4  0  0  0  0  4  4  0
 0  0  0  0  0  0  0  0  4  0  0  4  4  0  0  0  4  0  0  4  0  4  4  0  4  0  4  0  4  4  4
 0  0  0  0  0  0  0  0  0  4  0  0  0  4  0  4  0  4  4  4  0  4  4  0  4  0  0  4  4  0  4
 0  0  0  0  0  0  0  0  0  0  4  0  0  0  4  0  4  4  4  4  4  4  0  0  4  0  0  0  0  0  4

generates a code of length 31 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+113x^20+160x^22+908x^24+64x^25+1560x^26+640x^27+3924x^28+1984x^29+5456x^30+2816x^31+6005x^32+1984x^33+3520x^34+640x^35+2006x^36+64x^37+528x^38+316x^40+40x^42+36x^44+2x^48+1x^52

The gray image is a code over GF(2) with n=124, k=15 and d=40.
This code was found by Heurico 1.16 in 15.6 seconds.