The generator matrix

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

generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 187.

Homogenous weight enumerator: w(x)=1x^0+1068x^187+468x^188+2208x^191+894x^192+2544x^195+867x^196+2400x^199+726x^200+2112x^203+540x^204+1092x^207+327x^208+660x^211+231x^212+204x^215+36x^216+6x^220

The gray image is a linear code over GF(4) with n=264, k=7 and d=187.
This code was found by Heurico 1.16 in 3.6 seconds.