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

generates a code of length 77 over F4[X]/(X^2) who´s minimum homogenous weight is 210.

Homogenous weight enumerator: w(x)=1x^0+360x^210+480x^211+600x^212+792x^213+2460x^214+2640x^215+1548x^216+2232x^217+5256x^218+5736x^219+3075x^220+3468x^221+10332x^222+9444x^223+4815x^224+5928x^225+14616x^226+12024x^227+7665x^228+7920x^229+19080x^230+15552x^231+8325x^232+9084x^233+20004x^234+15864x^235+7581x^236+7620x^237+14868x^238+10932x^239+4908x^240+4224x^241+8184x^242+5592x^243+1905x^244+1488x^245+2772x^246+1464x^247+432x^248+228x^249+348x^250+144x^251+36x^252+24x^253+24x^254+27x^256+12x^260+21x^264+3x^268+3x^272+3x^284

The gray image is a linear code over GF(4) with n=308, k=9 and d=210.
This code was found by Heurico 1.16 in 329 seconds.