The generator matrix
1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X (a+1)X X (a+1)X
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a X (a+1)X+a+1 1 X (a+1)X (a+1)X (a+1)X+1 aX+1 aX+1 X+a aX+a+1 aX+a a+1 X+a aX+a+1 1 aX+a a+1 1 1 1 1
0 0 (a+1)X X aX X 0 (a+1)X aX (a+1)X (a+1)X X aX 0 (a+1)X 0 aX (a+1)X aX X (a+1)X 0 X aX 0 X (a+1)X 0 X X
generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.
Homogenous weight enumerator: w(x)=1x^0+765x^88+255x^96+3x^120
The gray image is a linear code over GF(4) with n=120, k=5 and d=88.
As d=88 is an upper bound for linear (120,5,4)-codes, this code is optimal over F4[X,sigma]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.031 seconds.