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

generates a code of length 73 over F4[X]/(X^2) who´s minimum homogenous weight is 199.

Homogenous weight enumerator: w(x)=1x^0+456x^199+1134x^200+852x^201+492x^202+2292x^203+3576x^204+3216x^205+900x^206+5004x^207+8157x^208+5976x^209+1872x^210+8928x^211+11865x^212+9192x^213+2856x^214+13104x^215+16680x^216+12996x^217+3528x^218+16620x^219+19644x^220+14292x^221+4044x^222+16128x^223+17181x^224+12192x^225+2880x^226+11784x^227+11931x^228+6432x^229+1440x^230+4536x^231+4902x^232+2160x^233+348x^234+984x^235+990x^236+276x^237+72x^238+36x^239+138x^240+24x^244+12x^252+9x^256+6x^260+6x^264

The gray image is a linear code over GF(4) with n=292, k=9 and d=199.
This code was found by Heurico 1.16 in 315 seconds.