The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+396x^161+552x^162+240x^163+9x^164+588x^165+444x^166+132x^167+27x^168+216x^169+336x^170+96x^171+21x^172+168x^173+216x^174+60x^175+300x^177+72x^178+24x^179+60x^181+108x^182+24x^183+6x^188

The gray image is a linear code over GF(4) with n=224, k=6 and d=161.
This code was found by Heurico 1.16 in 0.141 seconds.