The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+122x^74+20x^75+421x^76+268x^77+737x^78+304x^79+1015x^80+900x^81+1344x^82+896x^83+1572x^84+1344x^85+1619x^86+952x^87+1277x^88+848x^89+893x^90+364x^91+626x^92+212x^93+300x^94+24x^95+156x^96+12x^97+82x^98+36x^100+15x^102+15x^104+7x^106+1x^108+1x^110

The gray image is a code over GF(2) with n=340, k=14 and d=148.
This code was found by Heurico 1.16 in 92.4 seconds.