The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^24+60x^26+530x^28+496x^30+1392x^32+1352x^34+1847x^36+944x^38+925x^40+220x^42+245x^44+47x^48+1x^52+1x^56+1x^60

The gray image is a code over GF(2) with n=70, k=13 and d=24.
This code was found by Heurico 1.16 in 4.19 seconds.