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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 191.

Homogenous weight enumerator: w(x)=1x^0+672x^191+306x^192+1116x^195+312x^196+456x^199+168x^200+264x^203+96x^204+312x^207+81x^208+204x^211+45x^212+48x^215+12x^216+3x^228

The gray image is a linear code over GF(4) with n=264, k=6 and d=191.
This code was found by Heurico 1.16 in 0.093 seconds.