The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+268x^30+812x^32+1174x^34+1969x^36+2454x^38+2954x^40+2576x^42+1937x^44+1228x^46+729x^48+234x^50+45x^52+2x^54+1x^76

The gray image is a code over GF(2) with n=80, k=14 and d=30.
This code was found by Heurico 1.10 in 7.3 seconds.