The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+42x^29+155x^30+248x^31+339x^32+512x^33+656x^34+836x^35+943x^36+1024x^37+1250x^38+1374x^39+1424x^40+1428x^41+1325x^42+1192x^43+1045x^44+850x^45+596x^46+406x^47+303x^48+164x^49+103x^50+98x^51+40x^52+12x^53+11x^54+4x^55+1x^56+2x^59

The gray image is a code over GF(2) with n=80, k=14 and d=29.
This code was found by Heurico 1.10 in 6.97 seconds.