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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+80x^44+10x^46+172x^48+80x^50+207x^52+3072x^53+132x^54+160x^56+32x^58+86x^60+2x^62+49x^64+11x^68+1x^72+1x^88

The gray image is a code over GF(2) with n=424, k=12 and d=176.
This code was found by Heurico 1.16 in 0.499 seconds.