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

generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+87x^168+165x^172+189x^176+918x^180+2400x^184+87x^188+60x^192+48x^196+27x^200+60x^204+21x^208+12x^212+12x^216+6x^220+3x^240

The gray image is a linear code over GF(4) with n=244, k=6 and d=168.
This code was found by Heurico 1.16 in 0.201 seconds.