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

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+708x^177+720x^178+576x^179+678x^180+2076x^181+1836x^182+1404x^183+1635x^184+3384x^185+3060x^186+2340x^187+1824x^188+4632x^189+3444x^190+2448x^191+1917x^192+4896x^193+3804x^194+2508x^195+1998x^196+4716x^197+3120x^198+1812x^199+1482x^200+3000x^201+1800x^202+996x^203+624x^204+1056x^205+576x^206+192x^207+66x^208+108x^209+72x^210+12x^211+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 18.6 seconds.