The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  2  2  2  1  1  4  0  1  1  1  1  4  1  0  2  4  8  4  8
 0 12  0 12  8  4  8  4  0 12  0 12  8  4  8 12  4 12  4  0  8  4  0 12 12  4  8  4  0  8 12 12  4  0  4  4  4  4
 0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  0  8  8  0  8  8  0  8  0  0  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+14x^37+102x^38+6x^40+2x^45+2x^46+1x^48

The gray image is a code over GF(2) with n=304, k=7 and d=148.
This code was found by Heurico 1.16 in 0.0291 seconds.