The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  4  0  0  0  0  0  0  0  0  0  0  0  4  0  0
 0  0  4  0  0  0  0  0  0  0  0  0  0  4  0  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  4  0  0
 0  0  0  0  4  0  0  0  0  0  0  0  0  4  0  0
 0  0  0  0  0  4  0  0  0  0  0  0  0  4  0  0
 0  0  0  0  0  0  4  0  0  0  0  0  0  4  0  0
 0  0  0  0  0  0  0  4  0  0  0  0  0  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  0  0  0  4  0  0  0  4  0  0
 0  0  0  0  0  0  0  0  0  0  4  0  0  4  0  0
 0  0  0  0  0  0  0  0  0  0  0  4  0  4  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  4  4  0  0

generates a code of length 16 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+78x^4+728x^8+2002x^12+27150x^16+2002x^20+728x^24+78x^28+1x^32

The gray image is a code over GF(2) with n=64, k=15 and d=8.
This code was found by Heurico 1.16 in 1.09 seconds.