The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  8  1  1  1  1  2  0  2  1  1 12  4  1  1  0  1 12  1 12  1
 0  2  0  6  4 14 12  2  0  6 12 10  8  2 14  6  2  6 12 12 10  6  2  2  2 10  2  2 12  0  2  2  2 14  2 14
 0  0 12  0  4  4  8  4  0  8  0  8  4 12 12  4 12  8  4  0  0  8  8  4 12  4  0 12  8 12  0 12  0 12  0  8
 0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  8  8  0  0
 0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8
 0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  0  8  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+92x^31+167x^32+290x^33+431x^34+784x^35+635x^36+774x^37+390x^38+268x^39+142x^40+78x^41+8x^42+8x^43+12x^44+10x^45+2x^46+2x^48+1x^50+1x^52

The gray image is a code over GF(2) with n=288, k=12 and d=124.
This code was found by Heurico 1.16 in 8.87 seconds.