The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+12x^38+3x^40

The gray image is a code over GF(2) with n=144, k=4 and d=76.
This code was found by Heurico 1.16 in 0.0119 seconds.