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.