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

generates a code of length 65 over F4[X]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+828x^188+1566x^192+564x^196+420x^200+408x^204+234x^208+72x^212+3x^224

The gray image is a linear code over GF(4) with n=260, k=6 and d=188.
This code was found by Heurico 1.16 in 0.64 seconds.