The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  0  X  1  1  1  1  0  1  1  1  X  1  X  1 X^2  1  1  1  X  1  1 X^2 X^2+2
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  2  0 X^2+X X^2+X X^2 X^2 X+2  X X^2+X+2 X^2+X+2  2  X  X X^2+X  2  2 X+2  X  2 X^2+2 X^2+X X^2+X  X  0 X^2+X  X  2 X^2+X+2 X^2+X+2  X X^2+2  0  X  X
 0  0 X^2+2  0 X^2  0  0  2  0 X^2 X^2 X^2 X^2  2 X^2+2 X^2  0 X^2  2 X^2+2 X^2 X^2  2 X^2  2  2 X^2+2  0  2  0  2  0 X^2 X^2+2 X^2 X^2+2  0  2  0 X^2+2 X^2+2 X^2
 0  0  0 X^2+2  0  0  2 X^2 X^2 X^2 X^2+2  0 X^2+2 X^2  2 X^2+2 X^2  2 X^2 X^2+2  2 X^2+2  2  0  0  0 X^2  0 X^2  2 X^2+2 X^2  2  0 X^2+2 X^2  2 X^2 X^2+2  0  2 X^2
 0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  0  2  0  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  0  0  0  2  2  2  0

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+96x^37+205x^38+314x^39+497x^40+620x^41+687x^42+654x^43+477x^44+274x^45+140x^46+48x^47+14x^48+32x^49+17x^50+6x^51+3x^52+2x^53+6x^54+2x^55+1x^62

The gray image is a code over GF(2) with n=336, k=12 and d=148.
This code was found by Heurico 1.16 in 16.8 seconds.