The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1  2  2  3  0
 0  0  1  1  1  3  0  0
 0  0  0  2  0  2  4  0
 0  0  0  0  4  4  0  4

generates a code of length 8 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+37x^4+116x^5+370x^6+912x^7+1227x^8+904x^9+380x^10+112x^11+31x^12+4x^13+2x^14

The gray image is a code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0101 seconds.