The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+9x^52+27x^56+192x^57+24x^60+3x^76

The gray image is a linear code over GF(4) with n=76, k=4 and d=52.
This code was found by Heurico 1.16 in -3.24e-008 seconds.