The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+52x^78+112x^79+265x^80+250x^81+396x^82+234x^83+426x^84+222x^85+366x^86+218x^87+436x^88+184x^89+300x^90+164x^91+208x^92+88x^93+46x^94+26x^95+31x^96+14x^97+8x^98+8x^99+4x^100+10x^101+14x^102+4x^103+2x^104+2x^107+2x^108+2x^110+1x^112

The gray image is a code over GF(2) with n=344, k=12 and d=156.
This code was found by Heurico 1.16 in 1.47 seconds.