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

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+642x^172+600x^173+948x^174+1944x^175+1434x^176+1884x^177+1932x^178+3264x^179+2316x^180+2304x^181+2472x^182+4548x^183+2865x^184+2676x^185+2916x^186+4572x^187+3069x^188+2772x^189+2892x^190+4476x^191+2556x^192+2448x^193+1788x^194+2628x^195+1494x^196+900x^197+792x^198+984x^199+450x^200+240x^201+84x^202+120x^203+15x^204+3x^208+3x^216

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 seconds.