The generator matrix
1 0 1 1 1 2 1 1 0 0 1 1 1 0 1 2 1 1 0 1 1 1 0 1 1 X 1 X 1 X 1 X 1 1 X+2 X+2 1 1 1 1 1 X+2 1 0 1 1 1 1 0 1 1 1 0 X+2 X 1 1 1 1 1 X+2 X 1 1 0 1 2 0 1 1 1 X 1 1 1 1 2 1 X+2 X 2 1 1 0 2 1 X 2 2 X 0 1
0 1 1 0 1 1 2 X+1 1 1 0 X+3 3 1 0 1 2 1 1 1 0 3 1 X X+1 1 X 1 X+3 1 X 1 X+3 X+3 1 1 X+1 3 X+2 X+1 2 1 X+1 1 X 3 X+2 X+3 1 3 2 X 1 1 1 3 0 2 0 X+1 1 1 X 3 1 0 1 1 X+1 3 1 0 1 1 X+2 0 1 X 1 1 1 X 0 1 X X+2 X 1 1 X 1 0
0 0 X 0 0 0 0 2 2 2 0 0 2 X X+2 X+2 X X+2 X+2 X X+2 X+2 X+2 X+2 X+2 2 0 X+2 X+2 0 2 0 2 0 X+2 0 0 2 X+2 X+2 2 X+2 X+2 X 2 X X+2 0 X X 0 X+2 2 2 X+2 X+2 X 0 X+2 X+2 X+2 X+2 X 0 2 X X+2 2 X 2 X+2 X 2 2 X+2 2 0 0 0 X X X+2 0 X X+2 2 X X X+2 0 0 2
0 0 0 X 0 0 2 2 X X X+2 X+2 X+2 X+2 2 X+2 X+2 X+2 2 X X 0 0 0 X+2 0 0 2 X 2 0 X+2 X+2 2 2 X 0 0 2 X 0 X 0 X X 0 X X+2 0 X+2 X 2 0 2 2 X+2 X+2 2 0 X X+2 2 X 2 2 X X+2 X+2 2 2 X+2 0 X X X X+2 X 0 X+2 X+2 2 X+2 X 2 X X X 0 X 0 X+2 0
0 0 0 0 X X+2 X+2 2 X+2 0 X+2 0 X 2 X+2 X+2 X 0 X X+2 2 X 2 2 2 X+2 X+2 X+2 X 2 2 0 X+2 X 2 X+2 2 X X 0 X+2 X+2 0 0 2 X+2 X 2 X X X 0 0 X X 2 X+2 2 2 X+2 0 0 X 0 X 0 X 2 2 0 X+2 0 X+2 0 0 X 2 0 X+2 0 2 0 X+2 0 0 X 2 0 2 X 2 X+2
generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+40x^84+174x^85+248x^86+244x^87+305x^88+374x^89+352x^90+334x^91+298x^92+250x^93+261x^94+274x^95+260x^96+194x^97+165x^98+124x^99+62x^100+26x^101+18x^102+22x^103+13x^104+10x^105+8x^106+10x^107+8x^108+6x^109+3x^110+2x^112+6x^113+2x^116+1x^120+1x^122
The gray image is a code over GF(2) with n=368, k=12 and d=168.
This code was found by Heurico 1.16 in 1.67 seconds.