The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  X  1  2  X  1  X  X  2  2 2X  0  X 2X  2
 0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0

generates a code of length 31 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 32.

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

The gray image is a code over GF(2) with n=248, k=5 and d=128.
This code was found by Heurico 1.16 in 0.016 seconds.