The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+166x^32+382x^33+750x^34+1080x^35+1263x^36+1626x^37+1923x^38+1992x^39+1878x^40+1748x^41+1396x^42+1024x^43+599x^44+242x^45+179x^46+80x^47+29x^48+18x^49+8x^50

The gray image is a code over GF(2) with n=156, k=14 and d=64.
This code was found by Heurico 1.13 in 2.29 seconds.