The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+72x^37+216x^38+33x^40+144x^41+144x^42+24x^44+168x^45+216x^46+3x^48+3x^56

The gray image is a linear code over GF(4) with n=56, k=5 and d=37.
This code was found by Heurico 1.16 in -3.62e-008 seconds.