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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+33x^30+2x^31+59x^32+16x^33+64x^34+56x^35+63x^36+112x^37+55x^38+3212x^39+52x^40+112x^41+40x^42+56x^43+46x^44+16x^45+44x^46+2x^47+24x^48+16x^50+11x^52+3x^54+1x^62

The gray image is a code over GF(2) with n=312, k=12 and d=120.
This code was found by Heurico 1.16 in 0.29 seconds.