The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  2  1  2  1  1  2  1  2  1  2  1  2  1  1  1
 0  2  0  0  0  0  0  0  0  0  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  2  0  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  0  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2  0  0  0  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  2  0  0  2  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  0  2  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  2  2  0  0  2  0  0  2
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  2  2  2  2  0  0  2  0  2  0  0  2  0  0  2  0  0  2  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  2  2  0

generates a code of length 41 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+155x^28+480x^32+72x^34+995x^36+672x^38+1907x^40+1008x^42+1617x^44+288x^46+695x^48+8x^50+233x^52+49x^56+8x^60+4x^64

The gray image is a code over GF(2) with n=82, k=13 and d=28.
This code was found by Heurico 1.16 in 13.3 seconds.