The generator matrix

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

generates a code of length 64 over GR(16,4) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+255x^172+276x^173+264x^174+1068x^175+2757x^176+1764x^177+1308x^178+3264x^179+6738x^180+4404x^181+2388x^182+5604x^183+11835x^184+8220x^185+4500x^186+9924x^187+18249x^188+11388x^189+6300x^190+12756x^191+23946x^192+13548x^193+6720x^194+13536x^195+22962x^196+12300x^197+5628x^198+9948x^199+15195x^200+6996x^201+2868x^202+4356x^203+5592x^204+2352x^205+684x^206+864x^207+861x^208+192x^209+60x^210+120x^211+84x^212+24x^216+18x^220+21x^224+6x^228

The gray image is a code over GF(4) with n=256, k=9 and d=172.
This code was found by Heurico 1.16 in 229 seconds.