The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+190x^28+518x^30+1372x^32+2210x^34+3875x^36+4984x^38+6205x^40+5108x^42+4313x^44+2086x^46+1235x^48+426x^50+197x^52+28x^54+19x^56+1x^60

The gray image is a code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 60.2 seconds.