The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+336x^153+528x^154+444x^155+1020x^156+1440x^157+1908x^158+1548x^159+1917x^160+2748x^161+2976x^162+2064x^163+2745x^164+3504x^165+4392x^166+2460x^167+3093x^168+3876x^169+4404x^170+2928x^171+3360x^172+3660x^173+3624x^174+2040x^175+1962x^176+2256x^177+1836x^178+660x^179+624x^180+564x^181+300x^182+144x^183+117x^184+48x^185+6x^192+3x^196

The gray image is a linear code over GF(4) with n=224, k=8 and d=153.
This code was found by Heurico 1.16 in 15.5 seconds.