The generator matrix

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

generates a code of length 34 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+101x^22+168x^24+223x^26+64x^27+265x^28+192x^29+393x^30+576x^31+489x^32+1216x^33+8842x^34+1216x^35+601x^36+576x^37+363x^38+192x^39+280x^40+64x^41+200x^42+171x^44+99x^46+22x^48+14x^50+3x^52+4x^54+1x^58

The gray image is a code over GF(2) with n=136, k=14 and d=40.
This code was found by Heurico 1.16 in 5.35 seconds.