The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+186x^78+8x^79+94x^80+80x^81+204x^82+184x^83+61x^84+480x^85+142x^86+184x^87+52x^88+80x^89+132x^90+8x^91+32x^92+66x^94+13x^96+32x^98+2x^100+6x^102+1x^148

The gray image is a code over GF(2) with n=340, k=11 and d=156.
This code was found by Heurico 1.16 in 28.9 seconds.