The generator matrix

1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 2 1 2 2 0 1 1 2 1 1 1 2 1 1 0 1 1 2 2 0 2 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 2 3 2 1 1 3 2 1 3 2 2 2 1 0 2 1 0 1 0 0
0 0 1 0 0 0 0 0 0 1 1 1 1 0 2 1 2 0 2 3 2 3 1 2 3 1 2 1 2 2 0 3 2 2 2 0 3 2 0 0
0 0 0 1 0 0 0 0 1 0 3 2 1 1 1 1 2 2 3 3 3 3 3 1 0 0 2 3 3 1 0 3 3 2 1 2 1 2 0 0
0 0 0 0 1 0 0 0 1 1 0 2 3 2 0 0 3 2 1 0 3 3 0 2 1 3 1 2 2 2 0 1 1 1 2 3 0 2 0 0
0 0 0 0 0 1 0 1 0 1 3 2 3 1 1 2 3 0 1 1 3 0 0 1 3 2 3 2 3 0 0 3 2 0 2 0 1 0 0 0
0 0 0 0 0 0 1 1 3 2 0 3 1 1 2 1 2 1 0 3 2 1 2 1 2 2 3 1 0 1 1 3 3 0 2 2 3 3 2 0
0 0 0 0 0 0 0 2 2 0 2 0 2 0 2 2 2 2 0 0 0 0 2 2 0 2 2 2 0 0 0 0 2 2 2 0 2 2 0 0

generates a code of length 40 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+36x^27+67x^28+190x^29+341x^30+448x^31+681x^32+910x^33+1194x^34+1614x^35+1849x^36+2222x^37+2595x^38+2686x^39+2853x^40+2782x^41+2684x^42+2344x^43+1921x^44+1666x^45+1195x^46+884x^47+580x^48+370x^49+282x^50+166x^51+107x^52+50x^53+29x^54+14x^55+5x^56+2x^57

The gray image is a code over GF(2) with n=80, k=15 and d=27.
This code was found by Heurico 1.10 in 25.4 seconds.