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 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X^2 X^2 X X^2 1 1 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 X^2+2 0 X^2+2 0 X^2 2 0 X^2+2 2 X^2+2 2 X^2 2 X^2 X^2+2 0 X^2 2 0 X^2+2 0 X^2 2 X^2+2 2 X^2 0 X^2+2 0 X^2 2 X^2 0 X^2+2 2 X^2+2 0 X^2+2 0 X^2 2 X^2 0 X^2+2 0 X^2 0 2 X^2+2 X^2+2 2 0 2 X^2+2 X^2 0 2 X^2+2 X^2 0 2 2 2 X^2+2 X^2 X^2 X^2 0 2 2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 0 X^2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 0 2 2 2 2 2 0 2 0 2 2 0 2 2 0 0 2 0 2 2 2 2 2 0 0 2 2 2 0 2 0 2 0 2 2 0 2 0 0 0 0 2 0 2 0 2 2 0 0 2 2 0 0 0 2 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 0 2 0 0 0 0 0 2 2 2 2 0 2 2 2 2 2 0 2 2 0 2 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 0 0 0 0 2 0 0 2 0 2 2 2 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 0 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 2 0 2 2 0 2 0 0 2 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2 2 0 2 2 0 2 0 2 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 0 0 0 2 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 0 2 2 0 2 2 2 0 0 0 0 2 0 0 2 0 2 2 0 2 2 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 2 0 2 0 2 0 2 2 2 2 2 0 0 2 0 0 2 0 0 2 2 2 0 2 2 0 0 0 0 0 2 0 2 0 0 2 0 2 2 2 2 0 2 0 2 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 0 2 0 2 2 0 0 0 generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+56x^82+133x^84+348x^86+1040x^88+304x^90+74x^92+44x^94+31x^96+16x^98+1x^164 The gray image is a code over GF(2) with n=704, k=11 and d=328. This code was found by Heurico 1.16 in 10.2 seconds.