The generator matrix

 1  0  1  1  1  1  1  1  1  X  1  1  1  1 aX  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

generates a code of length 18 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+72x^53+144x^54+9x^56+24x^57+6x^60

The gray image is a linear code over GF(4) with n=72, k=4 and d=53.
As d=53 is an upper bound for linear (72,4,4)-codes, this code is optimal over F4[X,sigma]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in -3.24e-008 seconds.