The generator matrix

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

generates a code of length 32 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+178x^20+518x^24+192x^26+1281x^28+832x^30+10326x^32+832x^34+1401x^36+192x^38+461x^40+147x^44+21x^48+1x^52+1x^56

The gray image is a code over GF(2) with n=128, k=14 and d=40.
This code was found by Heurico 1.16 in 6.03 seconds.