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

generates a code of length 63 over GR(16,4) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+696x^178+708x^179+129x^180+1824x^182+1260x^183+309x^184+1752x^186+1308x^187+210x^188+1992x^190+1188x^191+99x^192+1356x^194+756x^195+123x^196+1044x^198+684x^199+108x^200+468x^202+204x^203+36x^204+84x^206+36x^207+6x^212+3x^216

The gray image is a code over GF(4) with n=252, k=7 and d=178.
This code was found by Heurico 1.16 in 1.26 seconds.