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

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+21x^36+32x^38+128x^39+67x^40+6x^44+1x^76

The gray image is a code over GF(2) with n=156, k=8 and d=72.
This code was found by Heurico 1.16 in 0.021 seconds.