The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  2  0  2  0  0  1  1  1  0  2  1  1  1  2  1  1  0  0  2  1  2  0  1  1  0  1  0  1  2
 0  1  0  0  0  1  2  0  0  1  1  1  1  0  2  1  3  2  1  1  1  1  3  1  1  1  0  1  0  1  3  1  2  2  2  0  1  2  1  0
 0  0  1  0  1  1  1  2  1  2  0  0  0  1  1  1  3  0  3  1  1  0  2  0  2  3  1  2  2  1  2  0  0  2  3  1  0  1  3  1
 0  0  0  1  1  0  0  1  3  3  2  3  2  2  3  3  1  3  2  0  1  2  2  1  3  1  2  1  1  1  2  0  1  1  0  0  3  1  2  3
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  2  0  0  0  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  2  2  0  2  2  0  0  2  2  2  0  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+104x^34+182x^36+209x^38+166x^40+92x^42+108x^44+86x^46+49x^48+20x^50+6x^52+1x^54

The gray image is a code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.16 in 0.115 seconds.