The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+312x^83+176x^84+594x^85+236x^86+588x^87+180x^88+540x^89+159x^90+316x^91+101x^92+266x^93+61x^94+190x^95+37x^96+148x^97+31x^98+54x^99+9x^100+32x^101+24x^102+22x^103+8x^104+4x^105+6x^107+1x^110

The gray image is a code over GF(2) with n=356, k=12 and d=166.
This code was found by Heurico 1.16 in 9.4 seconds.