The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+153x^16+252x^18+1097x^20+1620x^22+3329x^24+3416x^26+3415x^28+1640x^30+1078x^32+236x^34+127x^36+4x^38+15x^40+1x^44

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 6.41 seconds.