The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^20+76x^21+156x^22+286x^23+404x^24+566x^25+977x^26+1394x^27+2394x^28+3434x^29+4175x^30+4804x^31+4202x^32+3492x^33+2482x^34+1468x^35+971x^36+552x^37+354x^38+222x^39+142x^40+70x^41+45x^42+18x^43+20x^44+2x^45+3x^46+3x^48

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 16.4 seconds.