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

generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 194.

Homogenous weight enumerator: w(x)=1x^0+528x^194+468x^195+87x^196+768x^198+516x^199+99x^200+372x^202+204x^203+24x^204+276x^206+144x^207+3x^208+156x^210+108x^211+9x^212+156x^214+60x^215+30x^216+48x^218+36x^219+3x^232

The gray image is a linear code over GF(4) with n=268, k=6 and d=194.
This code was found by Heurico 1.16 in 0.11 seconds.