The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  X  1  1  0  1  1  1  1  1 aX  1  1  1  1  1  1  1  1  0  1  1 aX  1  1  1  1  1  1 (a+1)X  1  1 aX  1  1 (a+1)X aX  1  1  1  1  1  1  1  1  1 aX  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  X (a+1)X+a+1  1 (a+1)X+1  a  1  0 X+a (a+1)X+a+1 aX+1 X+a  1  X aX+a+1 X+1 X+a (a+1)X+1 (a+1)X+a+1 (a+1)X+a X+1  1 X+a aX  1 (a+1)X  1 X+a+1  X (a+1)X X+a+1  1  a aX+a+1  1  X a+1  1  1 (a+1)X+a+1  X  0 (a+1)X+1  0  0 aX+a (a+1)X+1 X+a+1  1  0
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX aX aX  0  0 aX aX (a+1)X (a+1)X aX aX  0 aX aX aX  X (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X  0 (a+1)X  X aX (a+1)X  X  0  0  X aX  X aX  X aX aX  X (a+1)X  0  0 aX (a+1)X  0  0  0 (a+1)X  X (a+1)X aX  X  0
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  X  0  X (a+1)X  0 aX  X  X (a+1)X (a+1)X (a+1)X (a+1)X  0 (a+1)X  X  X  0 aX (a+1)X aX  0 aX (a+1)X  X  0  X aX  X  0  0 (a+1)X (a+1)X  0  0 aX (a+1)X aX  0 (a+1)X (a+1)X aX  X  0 aX (a+1)X  X  0  X aX  X  X
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX (a+1)X  X  X (a+1)X (a+1)X aX  X (a+1)X  X  0  0  X  X (a+1)X  X (a+1)X  X  X  0  0  X aX (a+1)X  0 (a+1)X  0  0  X aX  0  0 (a+1)X  X  0 (a+1)X (a+1)X (a+1)X  X (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X  0 (a+1)X aX  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+105x^176+48x^177+180x^179+336x^180+540x^181+672x^183+621x^184+864x^185+924x^187+756x^188+1068x^189+1536x^191+630x^192+1488x^193+1548x^195+675x^196+1332x^197+1056x^199+585x^200+672x^201+228x^203+228x^204+132x^205+51x^208+24x^212+30x^216+27x^220+3x^224+15x^228+6x^232+3x^236

The gray image is a linear code over GF(4) with n=256, k=7 and d=176.
This code was found by Heurico 1.16 in 1.44 seconds.