The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  2  0  1  1  1  0  1  0  2  0  1  1  1  1  1  1  0  0  2  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  1  3  1  0  0  2  1  1  3  0  1  2  1  2  0  1  0  3  0  1  2  1  3  2  0
 0  0  1  1  1  0  1  0  1  1  2  0  3  1  0  1  1  0  0  1  1  1  2  1  0  1  3  2  1  3  1  0  1  1  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  0  2  0  2  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  2  0  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  2  2  0  0  2  0  2  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  0  0  2  0  0  2  2  0  2  0  0  2  2  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+59x^24+28x^25+126x^26+128x^27+238x^28+278x^29+349x^30+494x^31+511x^32+696x^33+766x^34+816x^35+721x^36+764x^37+546x^38+476x^39+399x^40+252x^41+223x^42+128x^43+96x^44+30x^45+33x^46+6x^47+22x^48+4x^50+1x^52+1x^58

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 3.67 seconds.