The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+53x^16+28x^17+210x^18+168x^19+460x^20+590x^21+1030x^22+1348x^23+1984x^24+2578x^25+2866x^26+3552x^27+3215x^28+3356x^29+2809x^30+2552x^31+1936x^32+1488x^33+1115x^34+536x^35+498x^36+150x^37+144x^38+36x^39+42x^40+2x^41+16x^42+3x^44+1x^46+1x^50

The gray image is a code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 22.1 seconds.