The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  2  2  0  1  0  0  0  2  1  2  1  1  1  1  2  2  1  2  2  1  0  1  1  2  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  2  1  1  1  1  1  1  3  0  1  1  2  3  0  1  1  1  2  2  1  3  2  1  1  2  2  0  2
 0  0  1  0  0  0  0  0  0  3  0  1  2  1  0  1  3  3  2  2  1  1  2  1  3  1  1  0  0  2  1  0  3  3  3  3  3  1  0  0  0
 0  0  0  1  0  0  0  0  3  1  2  1  1  2  1  0  0  1  2  3  0  2  3  3  3  3  0  0  2  2  0  2  1  2  2  2  0  1  1  1  0
 0  0  0  0  1  0  0  0  1  0  1  0  1  0  2  1  3  1  2  0  3  3  2  3  2  0  1  3  3  1  0  3  0  2  1  1  2  1  3  1  0
 0  0  0  0  0  1  0  1  0  3  3  3  1  0  2  1  1  3  3  1  2  3  1  0  2  0  2  1  3  2  1  1  1  2  1  0  1  2  2  0  1
 0  0  0  0  0  0  1  1  3  2  0  3  1  3  3  0  3  0  3  0  3  3  0  2  2  3  0  2  1  2  0  1  2  3  0  2  1  1  0  0  0
 0  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  0  2  2  2  0  2  2  0  2  2  2  0  2  2  2  0  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+58x^29+154x^30+340x^31+510x^32+636x^33+967x^34+1190x^35+1511x^36+1960x^37+2200x^38+2542x^39+2729x^40+2888x^41+2929x^42+2584x^43+2264x^44+1986x^45+1630x^46+1256x^47+893x^48+580x^49+405x^50+254x^51+151x^52+76x^53+32x^54+22x^55+3x^56+8x^57+3x^58+4x^59+2x^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 68.8 seconds.