The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^34+48x^35+51x^36+48x^37+37x^38+32x^39+31x^40+32x^41+42x^42+48x^43+34x^44+48x^45+15x^46+7x^48+1x^50+3x^52+3x^54+1x^56+1x^62

The gray image is a code over GF(2) with n=80, k=9 and d=34.
This code was found by Heurico 1.16 in 0.0319 seconds.