The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+263x^30+753x^32+1364x^34+1875x^36+2412x^38+2772x^40+2727x^42+2100x^44+1206x^46+630x^48+196x^50+57x^52+22x^54+2x^56+1x^58+1x^62+2x^64

The gray image is a code over GF(2) with n=80, k=14 and d=30.
This code was found by Heurico 1.16 in 37.2 seconds.