The generator matrix

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

generates a code of length 56 over F4[X]/(X^2) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+516x^157+684x^158+372x^159+54x^160+1032x^161+1584x^162+516x^163+60x^164+1536x^165+1404x^166+480x^167+48x^168+1464x^169+1236x^170+348x^171+42x^172+1452x^173+1128x^174+360x^175+27x^176+768x^177+588x^178+144x^179+6x^180+144x^181+288x^182+84x^183+6x^184+6x^188+6x^196

The gray image is a linear code over GF(4) with n=224, k=7 and d=157.
This code was found by Heurico 1.16 in 77.2 seconds.