The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3
 0  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+31x^30+448x^31+31x^32+1x^62

The gray image is a linear code over GF(2) with n=248, k=9 and d=120.
As d=122 is an upper bound for linear (248,9,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 9.
This code was found by Heurico 1.16 in 0.156 seconds.