The generator matrix

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

generates a code of length 29 over Z8 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+181x^16+668x^20+1524x^24+1280x^26+5292x^28+16384x^29+2560x^30+3127x^32+256x^34+1172x^36+284x^40+36x^44+3x^48

The gray image is a code over GF(2) with n=116, k=15 and d=32.
This code was found by Heurico 1.16 in 19 seconds.