The generator matrix

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

generates a code of length 43 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+96x^32+170x^33+275x^34+382x^35+517x^36+650x^37+816x^38+966x^39+992x^40+1216x^41+1326x^42+1396x^43+1367x^44+1262x^45+1146x^46+1012x^47+883x^48+634x^49+457x^50+302x^51+209x^52+150x^53+70x^54+38x^55+28x^56+12x^57+6x^58+3x^60+2x^61

The gray image is a code over GF(2) with n=86, k=14 and d=32.
This code was found by Heurico 1.10 in 7.86 seconds.