The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+62x^30+110x^31+245x^32+266x^33+375x^34+508x^35+675x^36+1270x^37+3125x^38+6058x^39+7390x^40+5954x^41+3208x^42+1390x^43+624x^44+466x^45+392x^46+240x^47+196x^48+108x^49+64x^50+14x^51+21x^52+5x^54+1x^66

The gray image is a code over GF(2) with n=320, k=15 and d=120.
This code was found by Heurico 1.16 in 13.7 seconds.