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

generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+101x^28+215x^32+64x^34+448x^36+2432x^38+492x^40+64x^42+147x^44+124x^48+7x^52+1x^68

The gray image is a code over GF(2) with n=152, k=12 and d=56.
This code was found by Heurico 1.16 in 0.761 seconds.