The generator matrix

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

generates a code of length 65 over F4[X]/(X^2) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+87x^180+168x^184+180x^188+933x^192+2385x^196+99x^200+72x^204+36x^208+30x^212+42x^216+21x^220+21x^224+6x^228+3x^232+3x^236+6x^240+3x^256

The gray image is a linear code over GF(4) with n=260, k=6 and d=180.
This code was found by Heurico 1.16 in 0.222 seconds.