The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+27x^26+40x^27+125x^28+154x^29+248x^30+398x^31+435x^32+870x^33+1629x^34+2610x^35+5690x^36+8172x^37+5754x^38+2692x^39+1713x^40+916x^41+413x^42+356x^43+177x^44+122x^45+108x^46+46x^47+42x^48+6x^49+11x^50+2x^51+8x^52+2x^54+1x^56

The gray image is a code over GF(2) with n=296, k=15 and d=104.
This code was found by Heurico 1.16 in 11 seconds.