The generator matrix

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

generates a code of length 67 over GR(16,4) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+54x^176+204x^180+411x^184+570x^188+1155x^192+2439x^196+4323x^200+4104x^204+1959x^208+330x^212+276x^216+192x^220+171x^224+111x^228+54x^232+18x^236+12x^240

The gray image is a code over GF(4) with n=268, k=7 and d=176.
This code was found by Heurico 1.16 in 3.01 seconds.