The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  X  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a  X (a+1)X+a+1  1  X aX+1 X+a
 0  0 (a+1)X  X aX  X  0 (a+1)X aX (a+1)X (a+1)X  X aX  0

generates a code of length 14 over F4[X,sigma]/(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 3.24e-008 seconds.