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

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

Homogenous weight enumerator: w(x)=1x^0+55x^36+144x^38+54x^40+1x^44+1x^72

The gray image is a code over GF(2) with n=152, k=8 and d=72.
This code was found by Heurico 1.16 in 0.0237 seconds.