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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+19x^54+70x^55+82x^56+92x^57+50x^58+292x^59+211x^60+842x^61+830x^62+840x^63+207x^64+282x^65+38x^66+60x^67+58x^68+46x^69+21x^70+18x^71+14x^72+18x^73+2x^76+2x^78+1x^108

The gray image is a code over GF(2) with n=496, k=12 and d=216.
This code was found by Heurico 1.16 in 0.596 seconds.