The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+54x^31+199x^32+408x^33+523x^34+998x^35+1197x^36+1986x^37+1697x^38+2340x^39+1674x^40+1914x^41+1173x^42+1138x^43+480x^44+294x^45+172x^46+76x^47+30x^48+6x^49+15x^50+3x^52+3x^54+2x^55+1x^58

The gray image is a code over GF(2) with n=156, k=14 and d=62.
This code was found by Heurico 1.16 in 6.13 seconds.