The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+252x^149+492x^150+432x^151+1245x^152+2052x^153+2688x^154+2088x^155+3420x^156+4956x^157+6084x^158+4440x^159+6681x^160+8892x^161+11640x^162+7860x^163+9972x^164+14112x^165+16608x^166+11508x^167+14070x^168+17868x^169+19776x^170+11808x^171+13083x^172+15660x^173+15060x^174+8112x^175+7908x^176+7812x^177+6264x^178+2628x^179+2553x^180+1980x^181+1212x^182+276x^183+360x^184+144x^185+48x^186+39x^188+27x^192+15x^196+9x^200+6x^204+3x^208

The gray image is a linear code over GF(4) with n=224, k=9 and d=149.
This code was found by Heurico 1.16 in 207 seconds.