The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+162x^76+550x^77+782x^78+1238x^79+1506x^80+1726x^81+2140x^82+2074x^83+2436x^84+2658x^85+2629x^86+2600x^87+2312x^88+2262x^89+2032x^90+1642x^91+1272x^92+950x^93+687x^94+420x^95+323x^96+194x^97+77x^98+52x^99+18x^100+10x^101+6x^103+2x^104+2x^105+3x^106+2x^110

The gray image is a code over GF(2) with n=344, k=15 and d=152.
This code was found by Heurico 1.13 in 21.9 seconds.