The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+51x^80+92x^81+138x^82+170x^83+83x^84+84x^85+88x^86+62x^87+84x^88+62x^89+41x^90+16x^91+11x^92+16x^93+7x^94+6x^95+2x^96+2x^97+4x^98+2x^99+1x^122+1x^126

The gray image is a code over GF(2) with n=340, k=10 and d=160.
This code was found by Heurico 1.16 in 0.393 seconds.