The generator matrix

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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+129x^172+12x^174+183x^176+144x^178+171x^180+648x^182+132x^184+1296x^186+108x^188+972x^190+72x^192+51x^196+42x^200+39x^204+27x^208+24x^212+33x^216+6x^220+3x^224+3x^232

The gray image is a linear code over GF(4) with n=248, k=6 and d=172.
This code was found by Heurico 1.16 in 0.207 seconds.