The generator matrix

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

generates a code of length 75 over F4[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+399x^208+372x^209+384x^210+288x^211+2046x^212+1392x^213+1056x^214+576x^215+3321x^216+2436x^217+1788x^218+984x^219+4593x^220+3204x^221+2196x^222+1068x^223+5031x^224+3372x^225+2376x^226+1332x^227+5190x^228+3552x^229+2328x^230+1128x^231+4704x^232+2556x^233+1500x^234+624x^235+2430x^236+1140x^237+564x^238+108x^239+717x^240+384x^241+96x^242+36x^243+147x^244+24x^245+27x^248+33x^252+15x^256+3x^260+6x^264+6x^268+3x^272

The gray image is a linear code over GF(4) with n=300, k=8 and d=208.
This code was found by Heurico 1.16 in 22.7 seconds.