The generator matrix

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

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+87x^28+192x^30+585x^32+384x^33+1152x^34+2400x^36+3456x^37+2304x^38+9687x^40+10368x^41+3456x^42+13791x^44+10368x^45+5184x^46+2004x^48+90x^52+27x^56

The gray image is a linear code over GF(4) with n=56, k=8 and d=28.
This code was found by Heurico 1.16 in 2.04 seconds.