The generator matrix

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

generates a code of length 41 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+64x^29+193x^30+284x^31+499x^32+674x^33+940x^34+1204x^35+1520x^36+1918x^37+2244x^38+2548x^39+2705x^40+2826x^41+2789x^42+2714x^43+2437x^44+2036x^45+1585x^46+1196x^47+850x^48+606x^49+382x^50+224x^51+154x^52+62x^53+58x^54+20x^55+25x^56+6x^57+1x^58+2x^59+1x^60

The gray image is a code over GF(2) with n=82, k=15 and d=29.
This code was found by Heurico 1.16 in 66.1 seconds.