The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+504x^171+624x^172+732x^173+948x^174+1944x^175+1515x^176+1632x^177+1992x^178+3312x^179+2208x^180+2400x^181+2568x^182+4296x^183+2736x^184+2832x^185+2640x^186+4872x^187+3186x^188+2628x^189+2748x^190+4440x^191+2802x^192+2352x^193+2208x^194+2544x^195+1395x^196+1032x^197+648x^198+1032x^199+306x^200+192x^201+72x^202+96x^203+72x^204+24x^205+3x^212

The gray image is a linear code over GF(4) with n=248, k=8 and d=171.
This code was found by Heurico 1.16 in 17.2 seconds.