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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+312x^155+456x^156+420x^157+84x^158+432x^159+486x^160+228x^161+60x^162+192x^163+246x^164+108x^165+24x^166+168x^167+279x^168+96x^169+12x^170+168x^171+51x^172+72x^173+12x^174+72x^175+75x^176+36x^177+3x^180+3x^192

The gray image is a linear code over GF(4) with n=216, k=6 and d=155.
This code was found by Heurico 1.16 in 2.08 seconds.