The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 179.

Homogenous weight enumerator: w(x)=1x^0+756x^179+291x^180+864x^183+312x^184+600x^187+192x^188+372x^191+87x^192+264x^195+90x^196+156x^199+48x^200+60x^203+3x^212

The gray image is a linear code over GF(4) with n=248, k=6 and d=179.
This code was found by Heurico 1.16 in 4.91 seconds.