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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 206.

Homogenous weight enumerator: w(x)=1x^0+504x^206+432x^207+606x^208+564x^209+2340x^210+1572x^211+1530x^212+1140x^213+3540x^214+2316x^215+2370x^216+1476x^217+4632x^218+2640x^219+2058x^220+1908x^221+5292x^222+2880x^223+2565x^224+1764x^225+4968x^226+2484x^227+2040x^228+1380x^229+4008x^230+1884x^231+1374x^232+708x^233+1764x^234+984x^235+654x^236+276x^237+528x^238+168x^239+108x^240+72x^242+6x^244

The gray image is a linear code over GF(4) with n=296, k=8 and d=206.
This code was found by Heurico 1.16 in 23.2 seconds.