The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 aX aX X (a+1)X 0
0 0 X 0 0 (a+1)X X 0 aX aX aX 0
0 0 0 X 0 X (a+1)X (a+1)X aX 0 aX 0
0 0 0 0 X (a+1)X aX X (a+1)X X 0 aX
generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+39x^24+177x^28+147x^32+3282x^36+291x^40+141x^44+18x^48
The gray image is a linear code over GF(4) with n=48, k=6 and d=24.
This code was found by Heurico 1.16 in 0.0152 seconds.