The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+76x^36+530x^37+1530x^38+2694x^39+3898x^40+4908x^41+5396x^42+5218x^43+4054x^44+2452x^45+1170x^46+522x^47+225x^48+44x^49+32x^50+14x^51+2x^52+2x^53

The gray image is a code over GF(2) with n=336, k=15 and d=144.
This code was found by Heurico 1.16 in 5.86 seconds.