The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+24x^29+86x^30+180x^31+406x^32+560x^33+717x^34+928x^35+1231x^36+1494x^37+1898x^38+2222x^39+2427x^40+2686x^41+2725x^42+2798x^43+2565x^44+2378x^45+1946x^46+1556x^47+1265x^48+872x^49+703x^50+448x^51+265x^52+166x^53+102x^54+58x^55+29x^56+10x^57+15x^58+2x^59+3x^60+2x^61

The gray image is a code over GF(2) with n=84, k=15 and d=29.
This code was found by Heurico 1.10 in 27.6 seconds.