The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1x^32+12x^33+2x^34

The gray image is a code over GF(2) with n=124, k=4 and d=64.
This code was found by Heurico 1.16 in 0.00683 seconds.