The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^2*X a^2*X  1  1  1  1  0 a^2*X  1 a*X  1 a*X  X  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  0  1  1  1  1  1  1  1  1  1 a*X  0  1  1  1  1  1  1  1  1  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2 a^2*X+1 a^2*X+1  a a^2*X+a^2 a^2  1  1 a^2*X+a  1 a^2*X+a^2  a  1  1 a*X+a^2 a^2*X  0  1  1  a X+1 a^2*X X+a a*X+1 a^2*X+1  0 a^2*X+a^2 X+a a^2*X+a^2  X a*X+a^2 a^2*X a*X  1 a^2*X+a^2 a^2*X+1 X+a^2 a*X+a a*X+a^2  a  1 a*X  1  1  1 a^2*X a^2  0 a^2*X+a^2  0 a^2*X  X X+a^2 a*X
 0  0  1  1  a a^2  1 X+1  1  a  0  X a*X+a a^2 X+1 a^2 X+a^2 a^2  0 X+a  a  0 a*X+1  1 X+a X+1 a*X+a^2 a^2 a^2*X  a X+a  1 a^2*X+a^2 X+a^2 a^2 a*X+1 X+a  X a*X  1  1 a*X+a a^2*X+1 X+a  X a^2*X+a^2 a*X+a a*X X+1  a a*X+a  1 a^2*X+a^2 X+a^2 a^2*X+a^2 a*X+a^2 a*X  X a*X+a^2  X  0 a^2
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a*X a*X a*X a^2*X a^2*X  X a^2*X a*X  X a*X a^2*X a^2*X  X a*X  0  X a*X a*X  X a*X  0  X  0  0  0 a^2*X  0 a^2*X  0 a^2*X  X a^2*X a*X a^2*X  X a*X a*X a^2*X a^2*X  0  X  0 a*X a*X a^2*X  X a*X  X a*X  X
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  0 a*X  X a*X  X a^2*X  X a*X  0  0 a^2*X  X  X a*X  X a*X a^2*X a^2*X  0  0  0  0 a*X  0 a^2*X  0 a^2*X a*X a^2*X a^2*X  X  0 a*X a*X a*X  0 a*X a^2*X a*X a^2*X a*X  0  0  X a^2*X a*X a^2*X a^2*X  X a^2*X

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

Homogenous weight enumerator: w(x)=1x^0+240x^169+180x^170+492x^171+654x^172+780x^173+984x^174+1548x^175+1227x^176+1752x^177+1824x^178+2664x^179+2139x^180+2364x^181+2772x^182+4212x^183+2478x^184+2964x^185+3300x^186+5376x^187+2904x^188+3156x^189+3408x^190+4356x^191+2235x^192+2784x^193+2088x^194+2184x^195+1155x^196+1044x^197+708x^198+636x^199+411x^200+228x^201+96x^202+36x^203+24x^204+48x^205+27x^208+15x^212+12x^216+18x^220+6x^224+3x^228+3x^232

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 20 seconds.