The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+116x^28+132x^29+351x^30+470x^31+784x^32+844x^33+1287x^34+1560x^35+1854x^36+2180x^37+2323x^38+2882x^39+2758x^40+3014x^41+2588x^42+2416x^43+1898x^44+1544x^45+1307x^46+850x^47+635x^48+316x^49+301x^50+136x^51+132x^52+32x^53+35x^54+6x^55+14x^56+2x^57

The gray image is a code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.10 in 26.6 seconds.