The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+124x^37+778x^38+1372x^39+2282x^40+2170x^41+3167x^42+2302x^43+2049x^44+1080x^45+649x^46+202x^47+139x^48+34x^49+21x^50+10x^51+1x^52+1x^54+2x^55

The gray image is a code over GF(2) with n=336, k=14 and d=148.
This code was found by Heurico 1.16 in 1.56 seconds.