The generator matrix

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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 202.

Homogenous weight enumerator: w(x)=1x^0+912x^202+756x^203+183x^204+1764x^206+1296x^207+195x^208+1728x^210+1344x^211+210x^212+1776x^214+1080x^215+180x^216+1332x^218+684x^219+99x^220+936x^222+600x^223+141x^224+588x^226+288x^227+12x^228+180x^230+96x^231+3x^240

The gray image is a linear code over GF(4) with n=284, k=7 and d=202.
This code was found by Heurico 1.16 in 85.8 seconds.