The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+44x^32+348x^33+759x^34+1088x^35+2012x^36+2472x^37+2999x^38+2332x^39+2292x^40+1114x^41+437x^42+274x^43+136x^44+28x^45+13x^46+16x^47+11x^48+6x^49+2x^51

The gray image is a code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 1.69 seconds.