The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  1  2 X+2  X  1  1  1  1  1 X+2  X  1 X+2 X+2  1  2  1  0  X  1  1  1  1
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0 X+1  1  2 X+3  1  1  1  1  3 X+2  X X+1  1  1  1  1  1  2  X  1  0  2  1  2  0 X+1
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  0  0  X X+2  X  0 X+2  X  2  0 X+2  0  2  X  X  2  0 X+2  X X+2  X  X X+2  X  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  2  0  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  2  0  2  0  0  2  2  0  0  0  0  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  0  2  2  2  2  2  0  0  2  0  0  2  0  2  0  2  2  0  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  2  0  2  2  2  2  2  0  2  2  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 29.

Homogenous weight enumerator: w(x)=1x^0+6x^29+63x^30+76x^31+207x^32+422x^33+534x^34+1026x^35+880x^36+2212x^37+1397x^38+2784x^39+1398x^40+2116x^41+884x^42+1164x^43+520x^44+342x^45+169x^46+68x^47+56x^48+22x^49+22x^50+2x^51+8x^52+3x^54+2x^56

The gray image is a code over GF(2) with n=156, k=14 and d=58.
This code was found by Heurico 1.16 in 6.71 seconds.