The generator matrix

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

generates a code of length 22 over GR(16,4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+216x^54+228x^55+441x^56+1260x^57+1344x^58+1452x^59+1719x^60+3420x^61+2832x^62+3588x^63+3966x^64+7236x^65+5568x^66+6756x^67+5157x^68+7860x^69+4632x^70+3336x^71+1983x^72+1728x^73+768x^74+33x^76+9x^80+3x^84

The gray image is a code over GF(4) with n=88, k=8 and d=54.
This code was found by Heurico 1.16 in 4.3 seconds.