The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+108x^169+204x^170+588x^171+399x^172+816x^173+1440x^174+1752x^175+687x^176+1596x^177+2520x^178+2748x^179+1038x^180+2568x^181+3804x^182+4248x^183+1452x^184+3000x^185+4860x^186+4512x^187+1443x^188+3504x^189+4680x^190+4248x^191+1275x^192+2508x^193+2832x^194+2556x^195+585x^196+1080x^197+1020x^198+792x^199+156x^200+180x^201+144x^202+60x^203+42x^204+33x^208+27x^212+12x^216+12x^220+6x^228

The gray image is a linear code over GF(4) with n=248, k=8 and d=169.
This code was found by Heurico 1.16 in 22.9 seconds.