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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 X 1 X 2 1 X 1 2 1 X 1 1 2 1 X 2 1 0 2 1 1 1 0 1 X 1
0 X 0 0 0 X X+2 X 2 2 X X+2 0 0 X X X X X 2 2 X+2 0 0 X 2 X+2 2 X+2 2 X+2 0 2 0 2 X+2 0 0 X X 0 2 X 0 X 2 X X 2 0 X 2 X+2 0 X X 2 X+2 2 2 X X+2 0 2 0 0 2 X X+2 X 0 X+2 0 0 X 2 X X 2 X X 2 2 2 X 0 X X+2
0 0 X 0 X X X 0 2 0 X+2 X X X+2 0 0 2 0 X X+2 2 X+2 2 X+2 X X 2 X+2 0 2 X 0 X 0 0 X+2 X X+2 X+2 2 X 0 2 X X 0 2 X+2 X+2 X+2 2 0 X+2 0 0 X+2 2 0 2 X 2 0 0 2 X X 2 2 2 X X+2 X X+2 0 0 X X+2 2 X+2 2 X 0 X X+2 2 2 0 0
0 0 0 X X 0 X X+2 0 X 2 X X 2 2 X+2 0 X 0 2 0 X X X+2 X+2 X 2 0 X+2 X+2 2 0 X 2 X 2 2 0 0 X 0 0 2 X X+2 X 0 X+2 X+2 2 0 X X+2 X X X+2 X X+2 0 X+2 X X X+2 X X+2 X+2 2 X 0 X X+2 X 0 0 X+2 X+2 2 X+2 X 2 X+2 0 X+2 2 X 2 X 0
0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 2 2 2 2 2 0 0 0 2 2 2 0 0 0 2 2 2 0 2 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 2 0 0 0 2 2 0 0 2 2 2 0 2 2 2 0 0 2 0 0 0 2 0 0 0 2 2 0 0 0 2 0
0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 0 2 0 2 0 0 0 2 0 2 0 0 0 0 2 2 0 2 2 0 2 2 2 0 2 2 2 2 0 0 0 0 2 2 2 0 0 0 2 0 2 0 0 0 2 2 0 0 2 2 0 2 2 2 2
generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+74x^80+168x^82+28x^83+220x^84+144x^85+256x^86+76x^87+234x^88+128x^89+194x^90+84x^91+157x^92+48x^93+80x^94+4x^95+75x^96+28x^98+27x^100+8x^102+11x^104+2x^106+1x^144
The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.917 seconds.