The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+53x^34+78x^35+99x^36+146x^37+148x^38+146x^39+154x^40+160x^41+134x^42+154x^43+158x^44+144x^45+128x^46+94x^47+77x^48+56x^49+37x^50+40x^51+23x^52+6x^53+12x^54

The gray image is a code over GF(2) with n=84, k=11 and d=34.
This code was found by Heurico 1.16 in 0.312 seconds.