The generator matrix

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

generates a code of length 64 over F4[X]/(X^2) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+504x^177+996x^178+636x^179+384x^180+1968x^181+2496x^182+1920x^183+990x^184+3096x^185+3372x^186+2004x^187+1017x^188+4608x^189+4536x^190+2856x^191+855x^192+4716x^193+4476x^194+3012x^195+954x^196+4392x^197+4116x^198+2208x^199+1113x^200+2808x^201+2136x^202+972x^203+273x^204+840x^205+804x^206+216x^207+30x^208+108x^209+108x^210+12x^212+3x^216

The gray image is a linear code over GF(4) with n=256, k=8 and d=177.
This code was found by Heurico 1.16 in 18.3 seconds.