The generator matrix

 1  0  0  0  1  1  1  2  1  1  1 2a+2  1  1  1  1  1 2a+2  2  1  1  1 2a+2
 0  1  0  0  2  1  3  1  a 3a+3 3a 2a+2 a+3  2 2a+1 3a 2a+3  1  1 2a+2  a  0  1
 0  0  1  0 2a+3  1 2a+2 2a+3 3a+2  a 2a+2  1 3a+3 a+3  0 2a+3 2a+1  2 3a a+2 3a+3 2a 3a
 0  0  0  1 3a+3  2 3a+1 3a+1 2a+2 2a+1 a+1 2a+3 3a+2  1 2a+1  3 a+3 3a a+2  0 a+3 3a+3 2a+3

generates a code of length 23 over GR(16,4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+360x^57+168x^58+432x^59+957x^60+2052x^61+1284x^62+1500x^63+2811x^64+4980x^65+2820x^66+3564x^67+5187x^68+8412x^69+5196x^70+5076x^71+6060x^72+7380x^73+2820x^74+1716x^75+1335x^76+1392x^77+24x^80+9x^84

The gray image is a code over GF(4) with n=92, k=8 and d=57.
This code was found by Heurico 1.16 in 4.5 seconds.