The generator matrix

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

generates a code of length 63 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+174x^172+132x^173+276x^174+972x^175+1134x^176+564x^177+876x^178+2748x^179+2148x^180+936x^181+1164x^182+4284x^183+3090x^184+1668x^185+1824x^186+5340x^187+3792x^188+2112x^189+1668x^190+5964x^191+4251x^192+2220x^193+1788x^194+5124x^195+3120x^196+1224x^197+1140x^198+2580x^199+1359x^200+348x^201+408x^202+612x^203+267x^204+12x^205+72x^206+24x^207+45x^208+30x^212+18x^216+21x^220+3x^224+3x^232

The gray image is a linear code over GF(4) with n=252, k=8 and d=172.
This code was found by Heurico 1.16 in 18.4 seconds.