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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+183x^152+189x^156+192x^159+135x^160+1152x^163+117x^164+1728x^167+102x^168+87x^172+54x^176+36x^180+33x^184+36x^188+30x^192+12x^196+6x^200+3x^212

The gray image is a linear code over GF(4) with n=220, k=6 and d=152.
This code was found by Heurico 1.16 in 0.205 seconds.