The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^34+594x^35+1224x^36+2618x^37+3984x^38+5166x^39+5324x^40+5462x^41+3914x^42+2464x^43+1092x^44+520x^45+172x^46+62x^47+39x^48+6x^49+6x^50+2x^51+2x^53

The gray image is a code over GF(2) with n=320, k=15 and d=136.
This code was found by Heurico 1.16 in 5.36 seconds.