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 0 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 2 1 1 1 1 1 1 1 X 0 1 1 0 1 2 1 0 1 X 1 1 1 0 X X 1 0 2 X
0 X 0 0 0 2 0 2 0 X X X X+2 X+2 X X 2 2 X+2 2 X+2 X X+2 0 0 X 0 X+2 2 X+2 X+2 2 2 X+2 X 2 X X 2 X+2 X+2 0 X+2 X+2 0 X+2 X+2 X+2 X+2 0 X 0 X+2 0 X 0 X X+2 0 2 X X X X+2 X 0 X 2 0 2 2 2 X X 0 X X X 0
0 0 X 0 0 2 X X X X+2 X 2 X+2 X 2 2 X+2 X 0 X 0 0 X 0 X+2 2 0 X+2 0 X X+2 2 X 0 0 0 X+2 X+2 X 2 X 2 X 2 X+2 2 X+2 X+2 2 0 0 2 2 X+2 X+2 X+2 2 2 X X X+2 0 X 0 X+2 0 X X+2 2 0 2 X+2 X 2 X+2 0 0 2 2
0 0 0 X 0 X X X+2 2 0 0 X+2 X X X 2 X 0 2 X+2 X 2 2 X 2 X 2 X+2 X 0 X 0 0 X+2 X+2 0 X+2 2 X+2 0 X 0 2 0 X+2 X X+2 X 0 X+2 X+2 X+2 X 2 2 X X 2 X X X+2 X X 0 X+2 X+2 X X+2 0 X+2 X X 0 2 X X+2 X+2 2 2
0 0 0 0 X X 2 X X+2 X 0 X+2 X 0 2 X X+2 X X 2 0 2 0 X 0 X+2 X 0 2 X+2 X+2 2 0 0 X 0 2 2 0 X X X X+2 2 X+2 X+2 2 2 0 X+2 0 2 0 X X+2 X 0 X+2 0 X+2 X+2 X+2 2 0 X 2 X+2 X+2 X X X+2 X X+2 X+2 X+2 X X+2 0 X+2
generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+135x^72+234x^74+349x^76+382x^78+386x^80+204x^82+172x^84+64x^86+61x^88+34x^90+15x^92+10x^94+1x^128
The gray image is a code over GF(2) with n=316, k=11 and d=144.
This code was found by Heurico 1.16 in 0.647 seconds.