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

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+444x^185+588x^186+216x^187+27x^188+528x^189+432x^190+204x^191+264x^193+252x^194+36x^195+9x^196+228x^197+240x^198+60x^199+24x^200+108x^201+144x^202+36x^203+84x^205+72x^206+24x^207+72x^209+3x^216

The gray image is a linear code over GF(4) with n=256, k=6 and d=185.
This code was found by Heurico 1.16 in 32 seconds.