The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+297x^172+192x^174+492x^175+828x^176+396x^178+852x^179+1095x^180+504x^182+1044x^183+1302x^184+648x^186+1752x^187+1515x^188+864x^190+1380x^191+1317x^192+396x^194+564x^195+483x^196+72x^198+60x^199+204x^200+39x^204+24x^208+18x^212+30x^216+6x^220+6x^224+3x^236

The gray image is a linear code over GF(4) with n=248, k=7 and d=172.
This code was found by Heurico 1.16 in 6.05 seconds.