The generator matrix

 1  0  0  0  0  0  1  1  1  2  1  1  2  1  2  0  0  0  1  1  1  1  1  2  0  1  1  0  1  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  3  0  1  1  1  1  2  0  3  1  2  1  1  2  0  2  0  3  1  1  1  0  0  0
 0  0  1  0  0  0  0  0  0  0  1  3  1  3  1  2  0  1  3  2  3  1  2  2  1  1  2  1  0  2  0  1  0  2  0
 0  0  0  1  0  0  0  1  1  1  0  3  3  3  3  1  2  0  0  3  1  3  3  0  3  1  0  2  2  3  0  0  1  1  3
 0  0  0  0  1  0  1  1  0  1  2  3  3  3  1  0  3  1  2  0  0  0  0  2  2  2  0  0  1  3  2  2  2  0  2
 0  0  0  0  0  1  1  0  1  1  2  1  1  2  2  2  0  1  0  3  0  3  2  3  0  2  1  1  3  1  3  0  0  1  1
 0  0  0  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  2  2  2  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  0  2  0  0  2  0  0  0  2  0  2  0  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+174x^25+407x^26+510x^27+893x^28+1140x^29+1552x^30+1924x^31+2281x^32+2652x^33+2867x^34+3294x^35+2919x^36+3034x^37+2456x^38+2016x^39+1554x^40+1038x^41+781x^42+418x^43+379x^44+144x^45+120x^46+28x^47+34x^48+8x^49+9x^50+2x^51+1x^52+2x^53

The gray image is a code over GF(2) with n=70, k=15 and d=24.
This code was found by Heurico 1.16 in 65.3 seconds.