The generator matrix

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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+828x^178+696x^179+168x^180+1476x^182+1236x^183+252x^184+2088x^186+1356x^187+162x^188+1956x^190+984x^191+195x^192+1260x^194+1128x^195+129x^196+972x^198+540x^199+63x^200+528x^202+180x^203+39x^204+108x^206+24x^207+6x^208+3x^212+3x^216+3x^220

The gray image is a linear code over GF(4) with n=252, k=7 and d=178.
This code was found by Heurico 1.16 in 17.3 seconds.