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

generates a code of length 72 over Z8 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+16x^73+8x^74+2x^76+4x^78+1x^80

The gray image is a code over GF(2) with n=288, k=5 and d=146.
This code was found by Heurico 1.16 in 0.117 seconds.