The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X
0 X 0 0 0 X 0 aX X aX 0 (a+1)X X X
0 0 X 0 0 (a+1)X X 0 (a+1)X (a+1)X X (a+1)X (a+1)X aX
0 0 0 X 0 X (a+1)X (a+1)X aX 0 aX aX (a+1)X (a+1)X
0 0 0 0 X (a+1)X aX X 0 aX (a+1)X (a+1)X aX (a+1)X
generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+147x^32+348x^36+1350x^40+1896x^44+276x^48+60x^52+18x^56
The gray image is a linear code over GF(4) with n=56, k=6 and d=32.
This code was found by Heurico 1.16 in 0.21 seconds.