The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  1 a*X  1  1  1  1  1 a^2*X  1  1  1  1  1  1  1 a*X  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2 X+a  1 a^2*X+1  0 a^2*X+a^2  1  X  a a^2*X+1  1 X+1 a^2*X+a^2  1  1 a*X+a^2  X X+a a^2*X a*X+a X+a^2 a*X+1 a*X+1 a^2*X+a a^2  1  1  X  1 a^2*X+a^2  a  1 X+1  1 a*X+a  X  1 a^2*X+a^2 a*X+1  1  a  0
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X a^2*X a^2*X a*X  X a^2*X  X a^2*X a^2*X  X  X a^2*X a*X  X a*X  X  0  0 a^2*X a^2*X a^2*X  X a^2*X a*X a*X a*X  0 a^2*X a^2*X  X  X a^2*X  X a*X a*X a^2*X a^2*X  X a^2*X  0 a*X  0
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0  0  X  X a*X a^2*X a^2*X  X  X  0  X  0  X  0 a^2*X a*X a*X  X a^2*X a*X a^2*X a*X a*X  X a*X a^2*X  0  X  X  0  0 a*X a^2*X a*X a*X a^2*X  0 a*X  X a*X a*X  0
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X  X  X a*X a^2*X  X a*X  0 a^2*X a*X  0 a^2*X a*X a^2*X  0  X a^2*X a*X  X  0 a^2*X a*X a*X  X a*X a^2*X a*X  X a^2*X  X a^2*X a*X a^2*X a^2*X  0 a*X  X a*X a*X a*X a*X a^2*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+72x^152+72x^154+228x^155+123x^156+792x^158+816x^159+201x^160+1380x^162+876x^163+144x^164+2064x^166+1296x^167+111x^168+2448x^170+1500x^171+93x^172+2040x^174+1104x^175+60x^176+420x^178+276x^179+63x^180+48x^183+54x^184+42x^188+30x^192+9x^196+15x^200+6x^204

The gray image is a linear code over GF(4) with n=224, k=7 and d=152.
This code was found by Heurico 1.16 in 1.21 seconds.