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

generates a code of length 60 over F4[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+30x^156+261x^160+381x^164+426x^168+192x^169+462x^172+1152x^173+363x^176+3072x^177+414x^180+4992x^181+399x^184+2880x^185+369x^188+279x^192+318x^196+165x^200+105x^204+84x^208+27x^212+6x^216+6x^220

The gray image is a linear code over GF(4) with n=240, k=7 and d=156.
This code was found by Heurico 1.16 in 2.62 seconds.