The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+34x^53+138x^54+224x^55+226x^56+572x^57+694x^58+1408x^59+1412x^60+2372x^61+2237x^62+2392x^63+1525x^64+1430x^65+624x^66+534x^67+124x^68+176x^69+112x^70+46x^71+34x^72+22x^73+23x^74+2x^75+2x^77+9x^78+2x^79+6x^80+2x^82+1x^90

The gray image is a code over GF(2) with n=496, k=14 and d=212.
This code was found by Heurico 1.16 in 12.2 seconds.