The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+306x^152+300x^153+528x^154+276x^155+1479x^156+1320x^157+1620x^158+684x^159+2811x^160+2508x^161+2748x^162+984x^163+4050x^164+3660x^165+3600x^166+1296x^167+4722x^168+4260x^169+4824x^170+1476x^171+4719x^172+3936x^173+3588x^174+1068x^175+3144x^176+2052x^177+1308x^178+336x^179+1014x^180+396x^181+216x^182+24x^183+186x^184+45x^188+24x^192+12x^196+6x^200+9x^204

The gray image is a linear code over GF(4) with n=224, k=8 and d=152.
This code was found by Heurico 1.16 in 15.9 seconds.