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

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+672x^175+987x^176+516x^177+1764x^178+1776x^179+2754x^180+1188x^181+2868x^182+2472x^183+3513x^184+1272x^185+3564x^186+3228x^187+4044x^188+1572x^189+4056x^190+3756x^191+4389x^192+1716x^193+3828x^194+2712x^195+3465x^196+876x^197+2508x^198+1872x^199+1449x^200+432x^201+828x^202+348x^203+342x^204+108x^205+60x^206+60x^207+45x^208+3x^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 18.5 seconds.