The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  1  1  X  1  1  1  1  X  1  1  X  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  0 a*X a*X  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  1  X a^2*X+1 X+a a*X+a^2  1  X  1 X+a a*X+a^2  1  X a*X+1  1 X+a a^2 a^2*X+1 a*X+1 X+1  0  a a^2*X a*X+a^2 a*X a*X+a a*X+a a^2*X+1 a*X+a a*X+a X+a a*X+a X+a  1 a^2*X+a a*X+1  1 a*X+1  1 a*X+1  a a^2*X+a^2 X+a^2 a^2 a^2*X+a^2 a^2 a^2 a*X+a^2  1  1  1  a
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X  0 a^2*X  0 a^2*X  0  X  X a*X a*X  X a^2*X a*X  X a*X a^2*X a*X  0 a^2*X a^2*X a*X a*X  0 a*X  X a^2*X a^2*X  X  0  X  0  X a*X  0  0  X a*X a*X  0 a*X  X a^2*X a*X  0  X a^2*X a^2*X  0 a^2*X  0  X  X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  X  0  0  X  X  X  0  0  X  X  X a*X a*X  0 a*X a*X a*X a^2*X  X  X  0 a^2*X a^2*X a^2*X a^2*X  0  X  0 a^2*X a^2*X a*X a^2*X a^2*X a*X a^2*X a^2*X  X  X a*X  0 a*X  0 a*X  0  0 a^2*X  0 a^2*X a*X a^2*X a^2*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+528x^188+264x^189+576x^191+873x^192+264x^193+384x^196+48x^197+384x^200+240x^204+168x^205+192x^207+144x^208+24x^209+6x^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 0.572 seconds.