The generator matrix

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

generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+225x^32+576x^36+216x^40+6x^48

The gray image is a linear code over GF(4) with n=48, k=5 and d=32.
This code was found by Heurico 1.16 in 0.172 seconds.