The generator matrix

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

generates a code of length 22 over GR(16,4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+96x^52+72x^53+552x^55+720x^56+852x^57+2544x^59+2118x^60+2736x^61+8256x^63+4713x^64+6696x^65+12048x^67+5697x^68+6888x^69+7320x^71+2859x^72+1188x^73+96x^76+72x^80+9x^84+3x^88

The gray image is a code over GF(4) with n=88, k=8 and d=52.
This code was found by Heurico 1.16 in 4.68 seconds.