The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+61x^38+62x^40+2x^46+1x^48+1x^54

The gray image is a code over GF(2) with n=156, k=7 and d=76.
This code was found by Heurico 1.16 in 0.017 seconds.