The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  0  X  1 a^2*X a*X  1  1  1  1  1  1  1  1 a*X  X a*X  1  1  1  1  1 a*X  1  1  X  1 a*X  1  1  X  1  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  X a*X  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a*X+a^2 a^2 a^2*X+1  1  1 a*X  1  1  1  X a^2*X+a^2 a^2*X X+1  0  X a^2*X+a^2  1  1  1 a^2*X+a^2 a^2*X+a^2 X+a a^2*X+1 X+a^2 a^2*X a^2 a^2*X+1  1 a*X  0 X+1 a^2*X+1  1  a a^2  a X+a^2 X+1 a^2  a  1 a^2*X+1  1 X+1 a*X+a  1  1 a*X+a  0  1  1 a^2*X
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a^2*X+a a^2  0 X+a  0 a*X a^2*X+1 X+a^2  a a^2*X+1 X+1 a^2*X+a^2 X+a^2  a a*X+a a*X+a^2 a*X a*X+a^2 a^2*X+1  X  X X+a X+a^2 a*X+a^2  1 X+1  1 a*X+a^2 a^2*X  1 a^2  0 a^2*X+1  X a^2 X+1 a*X+a a^2*X+a a^2*X+1  1 a*X+1 a^2*X+a^2 a*X a*X+a a^2*X+a^2  X a*X+a a*X+1 a^2 X+a a*X  0
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2 a^2*X+1  0 a*X a^2*X a^2*X+a^2 a^2*X+a^2 a^2*X+a^2  0 a*X+a a^2*X+1  a  X a*X+1 a*X+a^2  1 a^2*X+1 a*X+1 a^2*X+a a^2*X+1  X a^2*X+a^2  0 a^2*X+a  a X+a a*X a*X+a^2 a^2  1 a^2*X+1  X a^2 a^2*X  a a*X X+1 a^2*X+a X+a a*X+a^2 a*X+a^2 X+a^2 a*X+1 X+a a^2*X+1  a X+1  1 a^2 X+a a*X+a a^2*X+a^2  1
 0  0  0  0  X  0 a*X  0  0  0  X  X a*X a*X  X  X a*X a*X a^2*X a^2*X a*X  X a^2*X  X a*X  0 a^2*X  X  X a^2*X a^2*X  0  X a*X a*X  0  0  0  X  0  X  X  0 a*X a*X a*X a^2*X a^2*X  X a^2*X a^2*X a^2*X  0 a^2*X a^2*X a^2*X a*X  X a*X  0 a^2*X a*X  X a^2*X

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+285x^172+420x^173+480x^174+900x^175+2013x^176+1884x^177+2292x^178+2808x^179+5592x^180+4656x^181+4992x^182+5700x^183+8838x^184+7632x^185+7632x^186+9912x^187+14661x^188+11232x^189+10716x^190+13068x^191+17988x^192+13644x^193+12504x^194+14472x^195+17325x^196+11904x^197+10200x^198+10236x^199+11640x^200+7608x^201+4848x^202+3672x^203+4722x^204+2220x^205+1548x^206+624x^207+792x^208+240x^209+84x^210+48x^211+54x^212+18x^216+18x^220+15x^228+6x^232

The gray image is a linear code over GF(4) with n=256, k=9 and d=172.
This code was found by Heurico 1.16 in 230 seconds.