The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  1  1  2  2  1  1  1  1  1  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  0  0  8  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  0  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  0  0  8  0  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  8  0  8  0  8  8  8  0  8  8
 0  0  0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  0  8  0  0  8  0  0  8  0  0  8
 0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8
 0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  0

generates a code of length 31 over Z16 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+36x^18+123x^20+221x^22+248x^24+407x^26+1086x^28+1949x^30+24576x^31+1985x^32+1111x^34+420x^36+255x^38+192x^40+109x^42+34x^44+7x^46+6x^48+1x^50+1x^52

The gray image is a code over GF(2) with n=248, k=15 and d=72.
This code was found by Heurico 1.16 in 6.58 seconds.