The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+66x^78+228x^79+232x^80+550x^81+263x^82+454x^83+295x^84+436x^85+240x^86+280x^87+151x^88+210x^89+117x^90+216x^91+100x^92+88x^93+28x^94+68x^95+15x^96+22x^97+19x^98+2x^99+5x^100+4x^101+2x^102+1x^104+2x^105+1x^106

The gray image is a code over GF(2) with n=340, k=12 and d=156.
This code was found by Heurico 1.16 in 1.36 seconds.