The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^28+164x^29+280x^30+468x^31+724x^32+876x^33+1168x^34+1480x^35+1853x^36+2240x^37+2654x^38+2908x^39+2809x^40+2916x^41+2674x^42+2344x^43+2059x^44+1596x^45+1132x^46+868x^47+587x^48+364x^49+252x^50+112x^51+83x^52+32x^53+30x^54+12x^55+7x^56+4x^57+2x^58+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 60.3 seconds.