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 1 1 X 1 1 X 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 X 1 1 0 X^2+2 0 0 0 X^2 X^2+2 X^2 0 0 0 0 X^2 X^2+2 X^2 X^2+2 0 0 0 0 X^2 X^2 X^2+2 X^2+2 0 0 2 X^2+2 2 X^2 X^2+2 X^2 X^2 2 0 2 X^2+2 2 X^2+2 0 X^2 0 X^2+2 X^2 X^2+2 0 2 0 X^2+2 2 0 X^2+2 X^2 2 X^2 0 2 2 X^2 2 2 X^2 X^2+2 X^2+2 X^2 0 2 X^2+2 0 X^2 2 X^2+2 2 X^2 2 2 X^2 0 X^2+2 2 X^2+2 X^2+2 0 X^2+2 2 2 X^2 2 0 X^2 2 X^2 X^2 2 0 X^2 X^2+2 0 0 0 X^2+2 0 X^2 X^2 X^2+2 0 X^2 0 0 X^2+2 X^2 X^2+2 0 0 0 0 X^2 X^2+2 X^2 0 X^2+2 0 0 X^2 0 2 X^2 X^2+2 X^2+2 2 2 0 X^2 X^2 2 X^2 X^2 2 X^2+2 X^2+2 2 X^2+2 0 2 2 X^2 X^2 X^2+2 2 0 0 X^2+2 2 2 2 X^2+2 X^2+2 0 X^2+2 X^2 2 2 X^2+2 X^2+2 0 X^2 X^2+2 X^2+2 2 2 2 0 2 X^2 2 X^2+2 2 0 X^2+2 X^2 2 X^2 0 X^2+2 2 0 X^2 X^2 2 0 X^2+2 X^2+2 2 X^2+2 0 X^2 0 0 0 X^2+2 X^2 0 X^2+2 X^2 X^2 0 X^2+2 0 0 X^2+2 X^2 0 2 X^2 X^2+2 2 2 X^2+2 X^2 2 2 X^2+2 X^2 2 0 X^2 0 X^2+2 0 0 0 X^2 X^2 2 X^2+2 X^2+2 0 X^2+2 0 2 X^2 X^2+2 0 2 X^2+2 X^2 0 X^2 0 2 X^2+2 X^2 X^2+2 2 0 X^2+2 0 X^2+2 2 0 X^2 X^2 2 0 X^2+2 X^2+2 2 X^2 2 0 X^2 0 X^2 2 X^2+2 X^2+2 2 0 2 2 0 X^2+2 X^2 X^2 2 2 X^2+2 X^2+2 X^2+2 2 X^2 2 X^2+2 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 2 0 2 2 0 2 2 0 0 2 2 0 0 2 0 2 0 2 0 2 2 2 0 0 0 2 2 0 2 0 2 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 0 2 generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93. Homogenous weight enumerator: w(x)=1x^0+46x^93+79x^94+78x^95+78x^96+144x^97+1251x^98+148x^99+62x^100+48x^101+35x^102+24x^103+16x^104+16x^105+8x^106+4x^107+2x^108+2x^109+2x^110+2x^111+1x^112+1x^186 The gray image is a code over GF(2) with n=784, k=11 and d=372. This code was found by Heurico 1.16 in 113 seconds.