The generator matrix

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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+122x^28+381x^32+40x^34+826x^36+480x^38+1721x^40+1008x^42+1765x^44+480x^46+867x^48+40x^50+337x^52+99x^56+21x^60+3x^64+1x^68

The gray image is a code over GF(2) with n=84, k=13 and d=28.
This code was found by Heurico 1.16 in 13.4 seconds.