The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  2  2  2  1  1  1  1  1  1  1  1  2  2  2  2  2  1  1  1
 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  0  0  0  0  0  2  0  2  2  0  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  0  0  0  2  2  2  0  2  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0  0  2  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  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  0  2  2  0  2  2  2  0  0  2  2  0  2  2  2  0  0  2  0  2  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  0  0  0  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  2  0  2  2  0  0  0  0  0  0  0  0

generates a code of length 39 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+80x^24+44x^26+199x^28+4x^29+96x^30+40x^31+346x^32+180x^33+270x^34+480x^35+522x^36+840x^37+507x^38+1008x^39+481x^40+840x^41+502x^42+480x^43+272x^44+180x^45+355x^46+40x^47+113x^48+4x^49+194x^50+30x^52+65x^54+3x^56+14x^58+1x^60+1x^62

The gray image is a code over GF(2) with n=78, k=13 and d=24.
This code was found by Heurico 1.16 in 10.5 seconds.