The generator matrix

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

generates a code of length 22 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+21x^56+60x^57+216x^59+102x^60+288x^61+312x^63+363x^64+504x^65+648x^67+474x^68+576x^69+360x^71+21x^72+108x^73+18x^76+18x^80+6x^84

The gray image is a code over GF(4) with n=88, k=6 and d=56.
This code was found by Heurico 1.16 in 0.0258 seconds.