The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 158.

Homogenous weight enumerator: w(x)=1x^0+204x^158+168x^159+18x^160+240x^162+192x^163+33x^164+84x^166+6x^168+24x^170+3x^172+24x^174+24x^175+3x^184

The gray image is a linear code over GF(4) with n=216, k=5 and d=158.
This code was found by Heurico 1.16 in 0.531 seconds.