The generator matrix

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

generates a code of length 7 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+45x^2+20x^3+211x^4+240x^5+255x^6+2552x^7+255x^8+240x^9+211x^10+20x^11+45x^12+1x^14

The gray image is a code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00702 seconds.