The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+356x^80+834x^82+851x^84+612x^86+478x^88+390x^90+233x^92+160x^94+100x^96+52x^98+20x^100+9x^104

The gray image is a code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.11 in 0.637 seconds.