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

generates a code of length 68 over F4[X]/(X^2) who�s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+504x^196+1611x^200+714x^204+411x^208+375x^212+435x^216+36x^220+3x^224+3x^228+3x^240

The gray image is a linear code over GF(4) with n=272, k=6 and d=196.
This code was found by Heurico 1.16 in 0.166 seconds.