The generator matrix

 1  0  0  0  1  1  1  1  1  1  1 aX  1  1  1  1  1  1  1 aX  1  1  1  1  1  1  1  1  1 aX  1  1 aX  1  1  1 (a+1)X (a+1)X  X aX  0 (a+1)X  X  1  1  1  1  1  1  1  1 (a+1)X  1  1 aX  1  1  1 (a+1)X  X  1  1  1  1
 0  1  0  0  X aX  X (a+1)X (a+1)X aX aX  1  a  1 aX+a+1 aX+1 (a+1)X+a+1 aX+a (a+1)X+a  1 (a+1)X+1 (a+1)X+a X+a (a+1)X+1  1 X+a+1 aX+a  a a+1  1 (a+1)X+a aX+a+1  1 (a+1)X+a+1 aX aX+1  1  1  0 aX  1  1  1 aX+a (a+1)X+1  X aX+a+1 X+a aX+1 X+a+1  1  1 aX+a+1  0 (a+1)X (a+1)X+1 X+a aX+a  1  1 aX+a+1  X  1 aX+1
 0  0  1  0 (a+1)X+1 (a+1)X  a (a+1)X  0 aX+1 X+1 aX (a+1)X+a+1 (a+1)X+a aX+a+1  1 aX+1 a+1 X+a a+1 X+a+1 X+a+1 X+a (a+1)X+a+1 X+1 X+a  X  a  X X+a+1  1 X+a  X aX+a+1 (a+1)X+a  0  a (a+1)X+1  1  1 aX+a (a+1)X+a aX+a (a+1)X+1 aX X+a+1 (a+1)X+1 (a+1)X a+1  a  X aX+a+1 aX (a+1)X+a  1 X+a X+a+1  0  1  a aX+a (a+1)X+a X+a (a+1)X+1
 0  0  0  1 a+1  1 X+a+1  a aX+a+1 (a+1)X+a (a+1)X+1 (a+1)X+1 (a+1)X+a+1 X+a aX+1  X X+1 aX+a  1 aX+a+1 aX+a  0 X+a aX (a+1)X+a a+1 (a+1)X+1  0 (a+1)X+a+1 aX+a a+1 (a+1)X+a  a  0 (a+1)X (a+1)X X+1 (a+1)X  1 (a+1)X+a+1  X aX+a+1 (a+1)X+a X+a (a+1)X+1 (a+1)X+a (a+1)X+a+1 (a+1)X aX+a+1  1 a+1  X  1  1 (a+1)X+a aX+a+1 (a+1)X+1 a+1 X+a+1 aX aX+a  0  a (a+1)X+a+1

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

Homogenous weight enumerator: w(x)=1x^0+612x^177+864x^178+744x^179+483x^180+2004x^181+2088x^182+1380x^183+1047x^184+3636x^185+3372x^186+2148x^187+1263x^188+4680x^189+4200x^190+2580x^191+1545x^192+5136x^193+4452x^194+2208x^195+1338x^196+4152x^197+3792x^198+1968x^199+1026x^200+3048x^201+2124x^202+984x^203+414x^204+1212x^205+576x^206+264x^207+42x^208+96x^209+36x^210+12x^211+3x^212+3x^216+3x^220

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 16.9 seconds.