The generator matrix

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

generates a code of length 63 over F4[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+108x^175+504x^176+204x^177+252x^179+1284x^180+384x^181+504x^183+1614x^184+456x^185+684x^187+2106x^188+720x^189+540x^191+2409x^192+876x^193+660x^195+1605x^196+336x^197+288x^199+537x^200+96x^201+36x^203+48x^204+39x^208+24x^212+33x^216+18x^220+15x^224+3x^228

The gray image is a linear code over GF(4) with n=252, k=7 and d=175.
This code was found by Heurico 1.16 in 18.2 seconds.