The generator matrix

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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+552x^174+780x^175+543x^176+816x^177+1908x^178+2268x^179+1557x^180+1380x^181+2988x^182+3108x^183+2286x^184+1944x^185+3996x^186+3588x^187+2805x^188+2508x^189+4236x^190+3924x^191+3033x^192+1812x^193+4140x^194+3720x^195+2082x^196+1584x^197+2772x^198+1824x^199+834x^200+660x^201+804x^202+648x^203+153x^204+48x^205+108x^206+108x^207+15x^208+3x^212

The gray image is a linear code over GF(4) with n=252, k=8 and d=174.
This code was found by Heurico 1.16 in 17.4 seconds.