The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+57x^24+112x^25+180x^26+300x^27+430x^28+538x^29+746x^30+974x^31+1117x^32+1324x^33+1516x^34+1552x^35+1577x^36+1500x^37+1236x^38+996x^39+721x^40+560x^41+364x^42+244x^43+168x^44+58x^45+50x^46+30x^47+24x^48+4x^49+4x^50+1x^52

The gray image is a code over GF(2) with n=70, k=14 and d=24.
This code was found by Heurico 1.16 in 24.4 seconds.