The generator matrix

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

generates a code of length 30 over Z8 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+424x^16+176x^20+2157x^24+4944x^28+16384x^30+6745x^32+848x^36+866x^40+176x^44+46x^48+1x^56

The gray image is a code over GF(2) with n=120, k=15 and d=32.
This code was found by Heurico 1.16 in 11.2 seconds.