The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+142x^77+294x^78+446x^79+529x^80+592x^81+684x^82+670x^83+706x^84+626x^85+589x^86+558x^87+500x^88+474x^89+358x^90+296x^91+265x^92+180x^93+102x^94+64x^95+34x^96+24x^97+14x^98+14x^99+10x^100+8x^101+7x^102+2x^105+3x^108

The gray image is a code over GF(2) with n=340, k=13 and d=154.
This code was found by Heurico 1.16 in 5.21 seconds.