The generator matrix

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

generates a code of length 38 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+98x^24+57x^26+270x^28+156x^30+32x^31+392x^32+224x^33+302x^34+672x^35+501x^36+1120x^37+478x^38+1120x^39+455x^40+672x^41+532x^42+224x^43+237x^44+32x^45+354x^46+75x^48+122x^50+15x^52+34x^54+3x^56+11x^58+1x^60+2x^62

The gray image is a code over GF(2) with n=76, k=13 and d=24.
This code was found by Heurico 1.16 in 10.7 seconds.