The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+100x^34+198x^36+200x^38+146x^40+110x^42+110x^44+84x^46+49x^48+18x^50+8x^52

The gray image is a code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.10 in 0.031 seconds.