The generator matrix

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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+408x^197+444x^198+408x^199+1164x^200+1704x^201+1752x^202+1008x^203+2109x^204+2808x^205+2376x^206+1560x^207+2835x^208+3732x^209+2724x^210+1740x^211+3573x^212+3936x^213+3492x^214+1620x^215+3870x^216+4020x^217+3216x^218+1344x^219+2373x^220+3048x^221+1836x^222+1080x^223+1584x^224+1452x^225+864x^226+420x^227+363x^228+360x^229+156x^230+36x^231+36x^232+36x^233+36x^234+6x^236+6x^240

The gray image is a linear code over GF(4) with n=284, k=8 and d=197.
This code was found by Heurico 1.16 in 22 seconds.