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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+1272x^192+1308x^196+528x^200+504x^204+249x^208+108x^212+120x^216+3x^224+3x^240

The gray image is a linear code over GF(4) with n=264, k=6 and d=192.
This code was found by Heurico 1.16 in 137 seconds.