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

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+303x^184+168x^185+396x^187+1062x^188+192x^189+180x^191+360x^192+144x^193+294x^196+192x^197+225x^200+72x^201+180x^203+297x^204+12x^207+15x^208+3x^220

The gray image is a linear code over GF(4) with n=256, k=6 and d=184.
This code was found by Heurico 1.16 in 0.119 seconds.