The generator matrix

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

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+280x^79+202x^80+624x^81+216x^82+576x^83+188x^84+496x^85+122x^86+392x^87+103x^88+280x^89+58x^90+180x^91+75x^92+128x^93+6x^94+56x^95+34x^96+40x^97+14x^98+20x^99+5x^100

The gray image is a code over GF(2) with n=340, k=12 and d=158.
This code was found by Heurico 1.16 in 1.05 seconds.