The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+58x^39+172x^40+366x^41+439x^42+682x^43+688x^44+662x^45+492x^46+334x^47+95x^48+58x^49+25x^50+14x^51+4x^52+2x^53+1x^54+3x^62

The gray image is a code over GF(2) with n=352, k=12 and d=156.
This code was found by Heurico 1.16 in 0.172 seconds.