The generator matrix
1 0 1 1 1 1 1 1 1 X 1 1 1 1 aX 1 1 1 1 (a+1)X 1 1 1 1
0 1 (a+1)X+1 a (a+1)X+a+1 X aX+1 X+a aX+a+1 1 aX X+1 aX+a X+a+1 1 (a+1)X 1 (a+1)X+a a+1 1 0 X (a+1)X+1 aX+1
generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 70.
Homogenous weight enumerator: w(x)=1x^0+48x^70+150x^72+48x^74+9x^80
The gray image is a linear code over GF(4) with n=96, k=4 and d=70.
This code was found by Heurico 1.16 in -3.24e-008 seconds.