The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+32x^20+122x^22+12x^23+292x^24+216x^25+578x^26+412x^27+1120x^28+1776x^29+1927x^30+1912x^31+2619x^32+4336x^33+2947x^34+2680x^35+2666x^36+3104x^37+1917x^38+1020x^39+1184x^40+760x^41+589x^42+108x^43+244x^44+48x^45+97x^46+32x^48+13x^50+2x^52+1x^54+1x^58

The gray image is a code over GF(2) with n=68, k=15 and d=20.
This code was found by Heurico 1.16 in 34.8 seconds.