The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^29+178x^30+304x^31+489x^32+692x^33+946x^34+1186x^35+1594x^36+1906x^37+2247x^38+2558x^39+2709x^40+2778x^41+2686x^42+2720x^43+2364x^44+2122x^45+1704x^46+1192x^47+856x^48+556x^49+374x^50+206x^51+162x^52+82x^53+55x^54+26x^55+17x^56+6x^57+2x^58

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.