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 X X X 1 1 X X X 1 1 X 1 1 1 X 1 X 1 1 1 1 1 X 1 2 2 X 1 2 1 1 1 1 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 2 0 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 0 2 2 2 0 2 0 0 2 2 2 0 0 2 0 0 0 0 2 2 0 0 0 2 0 0 0 2 0 0 2 0 0 0 0 2 2 0 2 0 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 2 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 2 0 0 2 2 0 0 0 2 2 0 0 2 0 0 2 0 2 2 2 0 0 2 0 2 0 2 2 2 2 2 2 0 2 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 0 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 0 0 0 2 2 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 2 2 0 2 2 2 0 2 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 0 2 0 0 0 2 2 0 0 2 2 2 0 0 2 2 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 2 0 2 2 2 2 0 0 0 2 0 0 2 0 0 2 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 2 2 2 2 2 2 2 2 0 0 2 2 2 0 2 2 0 2 0 0 0 0 2 2 0 0 0 0 2 0 0 2 0 2 0 2 0 0 2 0 2 generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+101x^60+2x^62+211x^64+76x^66+316x^68+256x^69+172x^70+768x^71+365x^72+768x^73+192x^74+256x^75+249x^76+66x^78+150x^80+4x^82+85x^84+41x^88+16x^92+1x^116 The gray image is a code over GF(2) with n=288, k=12 and d=120. This code was found by Heurico 1.16 in 2.16 seconds.