The generator matrix

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

generates a code of length 34 over Z8 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+168x^24+186x^26+16x^27+765x^28+176x^29+1206x^30+656x^31+2485x^32+1200x^33+2644x^34+1200x^35+2424x^36+656x^37+1372x^38+176x^39+696x^40+16x^41+210x^42+106x^44+14x^46+10x^48+1x^60

The gray image is a code over GF(2) with n=136, k=14 and d=48.
This code was found by Heurico 1.16 in 5.97 seconds.