The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+253x^34+244x^35+546x^36+368x^37+541x^38+380x^39+494x^40+288x^41+433x^42+204x^43+214x^44+48x^45+51x^46+4x^47+21x^48+2x^50+4x^52

The gray image is a code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.16 in 14.9 seconds.