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

generates a code of length 65 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+102x^172+294x^176+417x^180+447x^184+405x^188+3507x^192+9591x^196+351x^200+312x^204+276x^208+258x^212+195x^216+114x^220+75x^224+30x^228+3x^232+3x^236+3x^256

The gray image is a linear code over GF(4) with n=260, k=7 and d=172.
This code was found by Heurico 1.16 in 2.92 seconds.