The generator matrix

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

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+285x^32+260x^33+746x^34+880x^35+1481x^36+1480x^37+2086x^38+1908x^39+2133x^40+1588x^41+1558x^42+760x^43+609x^44+256x^45+236x^46+36x^47+61x^48+12x^50+6x^52+2x^54

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 20.4 seconds.