The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  1  1  1  2  0  0  1  2  1  0  0  1  2  1  0  0  1  0  0  0  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  2  1  2  3  1  1  0  3  2  0  0  1  1  1  0  1  1  0  0  1  0  3  0  0  0
 0  0  1  1  1  0  1  0  1  1  0  0  1  1  2  1  3  0  3  0  1  0  1  0  1  0  2  1  2  1  1  1  1  0  1  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  2  0  2  2  2  0  2  0  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  0  2  0  2  2  0  2  2  2  0  0  0  2  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  2  0  0  2  0  2  2  2  0  2  2  0  0  0  0  0  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  0  2  0  0  2  0  2  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  2  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  0  2  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  2  0  0  0  0  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0  0  2  0  0  0  2  2  2  0  2  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+148x^24+84x^26+22x^27+550x^28+146x^29+611x^30+462x^31+1388x^32+1034x^33+1523x^34+1928x^35+2036x^36+2920x^37+1803x^38+3356x^39+1869x^40+2900x^41+2079x^42+1958x^43+1526x^44+1058x^45+1429x^46+438x^47+587x^48+130x^49+521x^50+28x^51+80x^52+4x^53+121x^54+7x^56+17x^58+4x^62

The gray image is a code over GF(2) with n=78, k=15 and d=24.
This code was found by Heurico 1.16 in 50.5 seconds.