The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+112x^28+78x^30+467x^32+472x^34+1091x^36+1100x^38+1490x^40+1208x^42+1029x^44+590x^46+316x^48+128x^50+85x^52+8x^54+14x^56+3x^60

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 4.56 seconds.