The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 X 0 X 1 1 X 1 X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 1 2 2X+1 0 2 2 0 2X+1 X X+1 1 2X 1 0 X+1 X+1 2 1 1 1 X+2 X 1 1 X X+2 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X X 0 2X 2X 2X X 0 2X 2X 0 2X 0 X X 0 0 X 2X 2X 0 2X 0 0 2X X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 X 2X 2X 0 2X 2X X 2X 0 X 2X X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 X 0 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 2X 0 2X X 0 2X 2X 0 2X X X X X 2X 2X X 0 X 2X 0 0 X 2X 2X 0 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 X 0 X 2X 0 2X 0 0 2X X 0 2X 0 2X X X 0 2X 0 2X 2X 0 0 2X 2X X X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X 0 X 0 X X X 2X X 0 X 2X 0 0 X 2X X 0 2X 2X 0 X 2X 2X 2X 2X X 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X X 2X 2X X X 0 2X 0 0 X 0 X X X X 2X 2X 2X 0 0 2X 0 2X 0 X X X 2X
generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 75.
Homogenous weight enumerator: w(x)=1x^0+50x^75+6x^77+196x^78+6x^79+42x^80+458x^81+108x^82+174x^83+952x^84+396x^85+510x^86+1680x^87+936x^88+1296x^89+3568x^90+1530x^91+2118x^92+5634x^93+2880x^94+2670x^95+7036x^96+3132x^97+2772x^98+6188x^99+2340x^100+2190x^101+3952x^102+1260x^103+1026x^104+1928x^105+462x^106+264x^107+648x^108+72x^109+54x^110+242x^111+168x^114+68x^117+24x^120+8x^123+4x^126
The gray image is a linear code over GF(3) with n=144, k=10 and d=75.
This code was found by Heurico 1.16 in 35.8 seconds.