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

generates a code of length 69 over F4[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+621x^200+792x^202+792x^204+360x^206+426x^208+240x^212+255x^216+360x^218+216x^220+24x^222+6x^224+3x^240

The gray image is a linear code over GF(4) with n=276, k=6 and d=200.
This code was found by Heurico 1.16 in 54.1 seconds.