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 X^2  1  1  1  1  1  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2 X^2  0  2 X^2+2 X^2+2  0  2 X^2 X^2  0 X^2  2  0  2 X^2+2 X^2+2  2  0  0  2  2 X^2+2 X^2
 0  0  2  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0
 0  0  0  0  2  0  2  2  2  0  2  0  2  0  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  2  0  2  2  0  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  2  2  0  0

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+87x^28+192x^30+512x^31+175x^32+56x^36+1x^60

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.031 seconds.