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  1 aX  1  0  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  1 (a+1)X+a+1  X  1  0  1 X+a X+a
 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 aX+1 (a+1)X+1 aX+a  a aX+a  1 (a+1)X  X
 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 aX+a  0 (a+1)X (a+1)X+a X+a+1 (a+1)X+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+492x^177+1116x^178+684x^179+699x^180+1824x^181+2412x^182+816x^183+1140x^184+3144x^185+4344x^186+1548x^187+1572x^188+3924x^189+5160x^190+1944x^191+1791x^192+4644x^193+5052x^194+1812x^195+1701x^196+3744x^197+4512x^198+1632x^199+1203x^200+2760x^201+2628x^202+660x^203+513x^204+876x^205+828x^206+120x^207+78x^208+96x^209+60x^210+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 30.1 seconds.