The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  0  1  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  0  1 a^2*X+1  0
 0  0 a^2*X  0  0  0  0  X  X  X a*X a*X  0 a*X
 0  0  0  X  0  0  X a^2*X a^2*X  0 a^2*X a*X a*X  0
 0  0  0  0 a^2*X  0 a*X  0 a*X a*X a*X a*X a*X a*X
 0  0  0  0  0  X a*X  X  0 a^2*X a^2*X a*X  X a*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+168x^28+48x^30+387x^32+384x^33+576x^34+2052x^36+3456x^37+2592x^38+9966x^40+10368x^41+5184x^42+14976x^44+10368x^45+3888x^46+756x^48+276x^52+90x^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 2.18 seconds.