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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+62x^51+125x^52+134x^53+237x^54+262x^55+412x^56+600x^57+503x^58+2790x^59+825x^60+4670x^61+677x^62+2716x^63+705x^64+610x^65+255x^66+240x^67+169x^68+100x^69+93x^70+68x^71+58x^72+30x^73+24x^74+4x^75+9x^76+1x^78+2x^79+1x^82+1x^90

The gray image is a code over GF(2) with n=488, k=14 and d=204.
This code was found by Heurico 1.16 in 16 seconds.