The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+100x^24+54x^26+350x^28+191x^30+624x^32+64x^33+429x^34+448x^35+935x^36+1344x^37+820x^38+2240x^39+1023x^40+2240x^41+1120x^42+1344x^43+667x^44+448x^45+782x^46+64x^47+283x^48+466x^50+93x^52+188x^54+17x^56+42x^58+3x^60+3x^62+1x^66

The gray image is a code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 19.5 seconds.