The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+230x^37+357x^38+458x^39+456x^40+478x^41+415x^42+396x^43+351x^44+324x^45+215x^46+218x^47+101x^48+54x^49+13x^50+16x^51+11x^52+2x^53

The gray image is a code over GF(2) with n=168, k=12 and d=74.
This code was found by Heurico 1.11 in 0.19 seconds.