The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+96x^151+420x^152+72x^153+324x^155+1203x^156+324x^157+396x^159+1749x^160+624x^161+660x^163+1986x^164+840x^165+696x^167+2724x^168+936x^169+588x^171+1605x^172+276x^173+252x^175+393x^176+60x^179+51x^180+27x^184+36x^188+21x^192+15x^196+9x^200

The gray image is a linear code over GF(4) with n=220, k=7 and d=151.
This code was found by Heurico 1.16 in 30.4 seconds.