The generator matrix

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

generates a code of length 68 over GR(16,4) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+453x^192+300x^193+372x^194+528x^195+1125x^196+492x^197+612x^198+624x^199+1530x^200+684x^201+708x^202+708x^203+1392x^204+588x^205+552x^206+480x^207+1089x^208+468x^209+360x^210+348x^211+819x^212+324x^213+288x^214+276x^215+588x^216+180x^217+144x^218+96x^219+162x^220+36x^221+36x^222+12x^223+3x^224+6x^228

The gray image is a code over GF(4) with n=272, k=7 and d=192.
This code was found by Heurico 1.16 in 1.23 seconds.