The generator matrix

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

generates a code of length 64 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+375x^176+756x^177+384x^178+1914x^180+2160x^181+1188x^182+3480x^184+3516x^185+1980x^186+5001x^188+4368x^189+2184x^190+6309x^192+4884x^193+2904x^194+6273x^196+4512x^197+2388x^198+3624x^200+3108x^201+1068x^202+1326x^204+1056x^205+192x^206+237x^208+216x^209+54x^212+36x^216+21x^220+18x^224+3x^228

The gray image is a linear code over GF(4) with n=256, k=8 and d=176.
This code was found by Heurico 1.16 in 19 seconds.