The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+46x^14+155x^16+304x^18+389x^20+451x^22+821x^24+1024x^25+1339x^26+3072x^27+1405x^28+3072x^29+1015x^30+1024x^31+708x^32+635x^34+503x^36+273x^38+103x^40+25x^42+7x^44+7x^46+4x^48+1x^50

The gray image is a code over GF(2) with n=56, k=14 and d=14.
This code was found by Heurico 1.16 in 5.75 seconds.