The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+64x^34+52x^35+161x^36+136x^37+281x^38+188x^39+289x^40+208x^41+267x^42+140x^43+168x^44+40x^45+21x^46+4x^47+13x^48+4x^50+7x^52+1x^54+1x^56+1x^58+1x^62

The gray image is a code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.141 seconds.