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

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+150x^184+288x^185+360x^186+168x^187+528x^188+348x^189+324x^190+84x^191+333x^192+192x^193+228x^194+48x^195+150x^196+84x^197+108x^198+60x^199+96x^200+192x^201+48x^202+84x^204+24x^205+72x^206+24x^207+60x^208+24x^209+12x^210+6x^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 0.094 seconds.