The generator matrix

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

generates a code of length 43 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+36x^29+90x^30+270x^31+484x^32+706x^33+963x^34+1320x^35+1941x^36+2482x^37+3066x^38+3706x^39+4324x^40+5046x^41+5376x^42+5522x^43+5507x^44+5062x^45+4557x^46+3912x^47+3229x^48+2418x^49+1795x^50+1416x^51+871x^52+562x^53+364x^54+222x^55+146x^56+70x^57+42x^58+14x^59+9x^60+2x^61+3x^62+2x^63

The gray image is a code over GF(2) with n=86, k=16 and d=29.
This code was found by Heurico 1.10 in 112 seconds.