The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+45x^44+112x^45+201x^46+420x^47+500x^48+1048x^49+1439x^50+2322x^51+3520x^52+4214x^53+4964x^54+4430x^55+3592x^56+2386x^57+1410x^58+906x^59+477x^60+398x^61+141x^62+102x^63+43x^64+30x^65+31x^66+12x^67+14x^68+4x^69+6x^70

The gray image is a code over GF(2) with n=432, k=15 and d=176.
This code was found by Heurico 1.16 in 17.2 seconds.