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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+75x^172+12x^174+204x^175+402x^176+192x^178+552x^179+957x^180+300x^182+1008x^183+1152x^184+672x^186+1176x^187+1272x^188+996x^190+1356x^191+1458x^192+672x^194+1176x^195+1164x^196+228x^198+600x^199+447x^200+72x^203+126x^204+27x^208+30x^212+27x^216+15x^220+9x^228+6x^232

The gray image is a linear code over GF(4) with n=252, k=7 and d=172.
This code was found by Heurico 1.16 in 1.41 seconds.