The generator matrix

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

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+258x^196+264x^197+216x^198+168x^199+600x^200+396x^201+240x^202+120x^203+339x^204+192x^205+192x^206+24x^207+288x^208+60x^209+36x^210+144x^212+156x^213+12x^214+48x^215+84x^216+72x^217+60x^218+24x^219+72x^220+12x^221+12x^222+3x^236+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 0.093 seconds.