The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1 X+2  0  1  0  1 X+2  1  2  1  1  X  1 X+2  X  1 X+2 X+2  1  1  1  1  X  2  1  1  1  2  2  1  0  1  X  1  X  1  1  1  1  1  0  X  1  1  0  1  2  X  1  1  1  1  1  1  2  1  1  1  1 X+2  0  X  X  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  0  0 X+3  1 X+1  1  3  1  3 X+3  1  1  X  1  3  X  1 X+2 X+3  1  X  1 X+2  3  X X+2 X+2  1 X+1  X X+1 X+2  1  1 X+2 X+2  3 X+1  1  1  X  2 X+3  1  2 X+2  2 X+3  1 X+1 X+2 X+1  3  1 X+2  0 X+1  2  0  1  X  1  0
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3  1  1 X+2 X+1 X+3 X+3  X X+2 X+2 X+3  2  2  2 X+2  3  1 X+1  3  1  0  0  1  1 X+1  X  3  2  0  0  1 X+2  1  X  3  X  1  2  3 X+2 X+2  1  3  2 X+1  1  0  2  3  0 X+3 X+3 X+3  0  X X+1 X+3 X+3  X X+2  3  0  0  0
 0  0  0  1  0  3  1  2  3  0 X+1  X  3  0 X+3  2  3 X+3  2 X+1 X+1  3  X  1  X  1  X X+2 X+3 X+1  X X+3 X+2  0  0 X+2  3  1 X+1  1  1  3  2  3 X+2  0  X X+1  1  X X+3  X  0  0  X  0  X  X  1  1  2  3 X+1  3  1  0  X X+2  1 X+2 X+2  1  3  0  3  2
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3  X  2  3 X+1  X X+3  1 X+2  1  X X+3  3 X+3 X+2  3  0  2  0  1 X+2  3  3 X+1  X X+2  2 X+1  X  1  3  2  1  3  3  3  0  3  0 X+2  0 X+2  X  X  1  3 X+2  2 X+2  0  3  0  X  3 X+1  X X+2  X  1  0  1 X+1  2

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+60x^66+422x^67+678x^68+1080x^69+1351x^70+1846x^71+2040x^72+2530x^73+2278x^74+2836x^75+2646x^76+2906x^77+2409x^78+2616x^79+1889x^80+1684x^81+1159x^82+958x^83+564x^84+386x^85+210x^86+118x^87+52x^88+22x^89+17x^90+2x^91+2x^94+2x^96+2x^98+2x^99

The gray image is a code over GF(2) with n=304, k=15 and d=132.
This code was found by Heurico 1.13 in 18.8 seconds.