The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  2  1  1  1  1  6 12 12  0  1 12 10  1  6  1  1
 0  1  1  4  3  1  2  7  1  5 14  1  6  9 11 12  1  1  1  0  7  2  1 15  1 11  4
 0  0  2  2  0  2  2 10  0  8  4  2  8  6 10 14 14  6  6  2  4  6  0  6  0  4  2
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  8  0  0
 0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  0  8  0

generates a code of length 27 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+125x^22+424x^23+930x^24+1936x^25+2556x^26+4480x^27+2530x^28+2000x^29+877x^30+344x^31+117x^32+32x^33+23x^34+6x^36+2x^38+1x^42

The gray image is a code over GF(2) with n=216, k=14 and d=88.
This code was found by Heurico 1.16 in 1.01 seconds.