The generator matrix

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

generates a code of length 63 over F4[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+696x^178+720x^179+201x^180+1896x^182+1152x^183+195x^184+1668x^186+1452x^187+162x^188+1992x^190+1116x^191+189x^192+1368x^194+840x^195+156x^196+1008x^198+600x^199+102x^200+492x^202+252x^203+6x^204+96x^206+12x^207+6x^208+3x^212+3x^216

The gray image is a linear code over GF(4) with n=252, k=7 and d=178.
This code was found by Heurico 1.16 in 1.61 seconds.