The generator matrix

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

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+134x^32+462x^33+616x^34+1214x^35+1179x^36+1836x^37+1585x^38+2136x^39+1799x^40+2062x^41+1197x^42+1052x^43+447x^44+362x^45+179x^46+72x^47+22x^48+12x^49+7x^50+6x^51+2x^52+2x^53

The gray image is a code over GF(2) with n=156, k=14 and d=64.
This code was found by Heurico 1.16 in 5.64 seconds.