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

generates a code of length 63 over F4[X]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+492x^174+828x^175+546x^176+840x^177+1956x^178+1944x^179+1731x^180+1440x^181+3072x^182+3240x^183+2448x^184+1896x^185+3768x^186+3768x^187+2460x^188+2328x^189+4392x^190+4032x^191+2799x^192+2088x^193+4224x^194+3504x^195+2097x^196+1392x^197+2700x^198+2064x^199+1008x^200+648x^201+852x^202+576x^203+210x^204+120x^205+48x^206+12x^207+6x^208+6x^212

The gray image is a linear code over GF(4) with n=252, k=8 and d=174.
This code was found by Heurico 1.16 in 22.9 seconds.