The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^20+650x^24+32x^26+1350x^28+896x^30+4051x^32+18624x^34+3882x^36+896x^38+1558x^40+32x^42+514x^44+140x^48+16x^52

The gray image is a code over GF(2) with n=136, k=15 and d=40.
This code was found by Heurico 1.16 in 24.3 seconds.