The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+30x^45+89x^46+74x^47+120x^48+190x^49+250x^50+454x^51+862x^52+1308x^53+1519x^54+1312x^55+847x^56+450x^57+210x^58+174x^59+62x^60+60x^61+85x^62+28x^63+23x^64+8x^65+17x^66+4x^67+4x^68+2x^69+3x^70+2x^71+1x^72+2x^74+1x^82

The gray image is a code over GF(2) with n=432, k=13 and d=180.
This code was found by Heurico 1.16 in 1.56 seconds.