The generator matrix

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

generates a code of length 55 over F4[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+90x^156+108x^157+144x^158+312x^159+408x^160+552x^161+192x^162+228x^163+264x^164+252x^165+48x^166+216x^167+174x^168+228x^169+72x^170+96x^171+123x^172+84x^173+96x^174+48x^175+114x^176+108x^177+24x^178+60x^179+39x^180+12x^181+3x^184

The gray image is a linear code over GF(4) with n=220, k=6 and d=156.
This code was found by Heurico 1.16 in 0.063 seconds.