The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+102x^79+197x^80+212x^81+177x^82+174x^83+207x^84+164x^85+142x^86+134x^87+108x^88+88x^89+106x^90+66x^91+45x^92+52x^93+15x^94+14x^95+12x^96+12x^97+3x^98+4x^99+5x^100+5x^102+2x^103+1x^116

The gray image is a code over GF(2) with n=340, k=11 and d=158.
This code was found by Heurico 1.16 in 0.738 seconds.