The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+38x^32+34x^33+147x^34+244x^35+351x^36+714x^37+695x^38+1618x^39+1200x^40+2500x^41+1368x^42+2544x^43+1056x^44+1636x^45+750x^46+668x^47+371x^48+218x^49+99x^50+44x^51+47x^52+18x^53+11x^54+2x^55+6x^56+2x^58+2x^60

The gray image is a code over GF(2) with n=168, k=14 and d=64.
This code was found by Heurico 1.16 in 7.98 seconds.