The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+93x^28+372x^30+798x^32+1314x^34+1810x^36+2358x^38+2731x^40+2512x^42+1968x^44+1278x^46+691x^48+320x^50+88x^52+32x^54+11x^56+6x^58+1x^60

The gray image is a code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.10 in 6.69 seconds.