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

generates a code of length 28 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+65x^20+186x^24+128x^26+1306x^28+128x^30+156x^32+69x^36+8x^40+1x^48

The gray image is a code over GF(2) with n=112, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0985 seconds.