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

generates a code of length 68 over GR(16,4) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+93x^180+279x^184+480x^188+663x^192+1473x^196+2934x^200+4173x^204+3720x^208+1518x^212+300x^216+213x^220+204x^224+174x^228+96x^232+30x^236+24x^240+6x^244+3x^248

The gray image is a code over GF(4) with n=272, k=7 and d=180.
This code was found by Heurico 1.16 in 3.09 seconds.