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

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+129x^164+390x^168+447x^172+873x^176+1983x^180+4101x^184+4680x^188+2538x^192+387x^196+273x^200+225x^204+198x^208+105x^212+36x^216+12x^220+6x^224

The gray image is a linear code over GF(4) with n=248, k=7 and d=164.
This code was found by Heurico 1.16 in 2.77 seconds.