The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  2  1  1  X  X  1  2  1  1  0  1  X  1  1  1 X+2  1  1  X  1  0 X+2 X+2  1  1  1 X+2  1
 0  1  0  0  1  1  1  X  2  3  1  1  2  3  0 X+2  1  1  2  X  1  1  2  2 X+2 X+1  1 X+2 X+3  1  1  X  1  X X+1  1  X  1 X+3
 0  0  1  1  2  3  1  1  X X+2  X X+3 X+1 X+3  1  1  X  1  3 X+2  2 X+1  1  2  1 X+2  3  0  0 X+3  1  1 X+2  1 X+1  0 X+3  X  2
 0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  2  2  2  2  0  2

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+273x^36+320x^38+249x^40+64x^42+55x^44+48x^46+14x^48

The gray image is a code over GF(2) with n=156, k=10 and d=72.
This code was found by Heurico 1.11 in 0.0298 seconds.