The generator matrix

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

generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+693x^208+924x^209+708x^210+564x^211+3363x^212+3240x^213+2484x^214+1692x^215+7809x^216+5592x^217+4536x^218+2484x^219+13551x^220+8832x^221+6516x^222+3432x^223+18495x^224+12660x^225+9024x^226+4836x^227+22650x^228+15300x^229+10260x^230+4860x^231+22476x^232+13884x^233+8772x^234+3900x^235+16167x^236+8760x^237+5004x^238+2112x^239+7206x^240+3408x^241+1620x^242+600x^243+2016x^244+1020x^245+216x^246+96x^247+180x^248+108x^249+12x^250+36x^252+15x^256+3x^260+15x^264+6x^268+6x^272

The gray image is a linear code over GF(4) with n=304, k=9 and d=208.
This code was found by Heurico 1.16 in 407 seconds.