The generator matrix

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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 205.

Homogenous weight enumerator: w(x)=1x^0+144x^205+264x^207+1239x^208+192x^209+264x^211+669x^212+144x^213+48x^215+36x^216+144x^217+9x^220+96x^221+168x^223+561x^224+48x^225+24x^227+39x^228+3x^236+3x^240

The gray image is a linear code over GF(4) with n=284, k=6 and d=205.
This code was found by Heurico 1.16 in 12.2 seconds.