The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  1  1  0  1  0  1  2  0  1  2  1  0  0  1  1
 0  1  1  0  1  1  0  1  1  0  3  1  0  3  1  0  3  1  0  3  0  3  1  3  1  0  1  1  3  1  2  2  1  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  0  0  2  0  2  2  2  0  2  2  2  0  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  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  2  0  0  2  0  2  0  2  0  0  2  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  2  0  0  2  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  0  2  2  0  2  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  0  0  2  0  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  0  2  0  2  0  0  2  0  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+82x^24+38x^26+308x^28+286x^30+656x^32+604x^34+858x^36+476x^38+469x^40+126x^42+144x^44+6x^46+39x^48+2x^52+1x^56

The gray image is a code over GF(2) with n=70, k=12 and d=24.
This code was found by Heurico 1.16 in 1.05 seconds.