The generator matrix

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

generates a code of length 75 over F4[X]/(X^2) who´s minimum homogenous weight is 209.

Homogenous weight enumerator: w(x)=1x^0+420x^209+540x^210+636x^211+801x^212+2016x^213+1788x^214+1476x^215+1479x^216+2868x^217+2496x^218+2280x^219+1779x^220+3924x^221+2844x^222+2652x^223+2445x^224+4284x^225+3108x^226+2580x^227+2094x^228+4404x^229+2664x^230+2004x^231+1935x^232+3060x^233+2160x^234+1464x^235+843x^236+1428x^237+1044x^238+588x^239+348x^240+600x^241+240x^242+144x^243+51x^244+36x^245+12x^246

The gray image is a linear code over GF(4) with n=300, k=8 and d=209.
This code was found by Heurico 1.16 in 23 seconds.