The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1 12  1  2  1  1  1  1  1  6  0  1  1 10  1  1  1  2  1 14  1  0  4  1 14  2  1  2  8  1  1  1
 0  1 11  6 13  1  0  3  1  6  1  5  2  1  7  1  4 13 11  0  6  1  1  6  9  1  3  4 10  1 12  1 11  1  1 15  1  1 12  2  2 10 10  0
 0  0 12  0  4  0  0  4  8  0  8  4  0  0  4  8  8  0  8  4 12  4 12  4  4  4  0 12  0  4 12 12  0  8  8  0  0  4  8  0 12 12 12  4
 0  0  0 12  0  0 12  4 12  8  4  4 12  8  0  4  4 12 12 12 12 12  4 12 12  4  8  8  8  0  4  8 12  8 12  0 12  8  0  4 12  4  4 12
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  0  8  8  8  0  0  8  8  0  8  8
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  8  0  0  0  0  0  0  0
 0  0  0  0  0  0  8  8  8  0  0  8  0  0  0  0  8  8  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  0  0  0  8  0  8  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+65x^36+112x^37+241x^38+488x^39+1207x^40+2304x^41+3756x^42+5348x^43+5907x^44+5192x^45+3705x^46+2384x^47+1196x^48+420x^49+205x^50+100x^51+64x^52+32x^53+24x^54+8x^56+4x^57+3x^58+2x^62

The gray image is a code over GF(2) with n=352, k=15 and d=144.
This code was found by Heurico 1.16 in 8.25 seconds.