The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+144x^28+96x^29+156x^30+516x^31+1224x^32+1860x^33+1440x^34+2640x^35+7413x^36+13296x^37+6264x^38+14328x^39+28698x^40+37848x^41+13248x^42+30480x^43+40794x^44+37776x^45+9612x^46+7332x^47+5601x^48+1284x^49+81x^52+12x^56

The gray image is a linear code over GF(4) with n=56, k=9 and d=28.
This code was found by Heurico 1.16 in 26.6 seconds.